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SYSTEM 

OF 

GEOMETRY AND TRIGONOMETRY 

TOGETifER WITH A 

TREATISE OJV* SURVEriJ^TG; 

-REACHING VARIOUS WAYS OF TAKING THE SURVEY OP A FIELD 
ALSO TO PROTRACT THE SAME AND FIND THE AREA. 

LIKEWISE, 

RECTANGULAR SURVEYING: 

OB, 

AN ACCURATE METHOD OF CALCULATING THE AREA OF 

ANY FIELD ARITHMETICALLY, WITHOUT THE 

NECESSITY OF PLOTTING IT. 

TO THE WHOLE ARE ADDED, 

SEVERAL MATHEMATICAL TABLES, 

NECESSARY FOR SOLVING QUESTIONS IN 

TRIGONOMETRY AND SURVEYING ; 

WITH A PARTICULAR EXPLANATION OF THOSE TABLEJ^ 
AND THE MANNER OF USING THEM. 

COMPILED FROM VARIOUS AUTHORS, 

BY ABEL FLINT, A.BL 



ftFTH EDITION, WITH IMPORTANT ADDITIONS, 

BY GEORGE GILLET, 

SURVEYOR GENERAL OF THE STATE OF CONWECTlCUt. 



HARTPOllD : 

PITBLISHEP BY OLIVER D. COOKE & CO. 

1825. 






district of Conneeticui, ss. 

BE IT REMEMBERED, That on the twenty-fifth day of Septcmbet, 
in the forty-third year of the Independence of the United States of 
America, OliTer D. Cooke & Co., of the said district, have deposited in this 
office the title of a book, the right whereof they claim as Proprietors, in the 
words following, to wit— 

" A System of Geometry and Trigonometry: together with a Treatise o». 
Surveying ; Teaching various ways of taking the Survey of a Field ; Also to 
Protract the same and find the Area. Likewise, Rectangular Surveying ; 
or, an Accurate Method of calculating the Area of any Field Arithmeticafly 
without the necessity of Plotting it. To the whole are added several 
Mathematical Tables, necessary for solving Questions in Trigonometry and 
Surveying ; with a particular explanation of those Tables, and the Manner 
of using them. Compiled from various Authors. By Abel Flint, A. M. 
Fifth Edition, with important Additions, By tJeorge Gillet, Surveyor General 
of the State of Connecticut." 

•^ In conformity to the Act of the Congress of the United States, entitled 
" An Act for the encouragement of Learning, by securing the copies of 
Maps, Charts, and Books, to the authors and proprietors of such copies, 
donns the times therein mentioned." 

R. I. INGERSOLL, 
Clerk of the District of Connecticut. 
A true copy of Record, examined and sealed by me, 
r r I r J R- 1- INGERSOLL, 

J ^!,'"\^S ^M^ ' ^terR of the Histrict of CmriMimt 



"fo-x^nx 



RECOMMENDATIONS 



HAVING perused, with some attention, the following 
Treatise on Surveying, in Manuscript, it appears to me 
to be estimable for its simplicity and perspicuity ; and, 
by excluding all matter but remotely connected with 
the main subject, and reducing the Tables of Log- 
arithms, of Logarithmic Sines, Tangents, and Secants, 
and of Difference of Latitude and Departure, without 
impairing their use, in their application to most cases 
which occur in common Surveying, and supplying any 
possible defect by a Table of Natural Sines, to com- 
prise, in the limits of a pocket volume, whatever is 
most essential and most useful in the Art, including the 
important modern improvement ot Rectangular Sur- 
veying ; and on the whole, particularly from the size 
of the volume, to be well adapted to general use. 

JOHN TREADWELL, 

Farmington, Sept. 20th, 1804. 



RECOMMENDATIONS. 

WE the subscribers have carefully perused a Trea-- 
tise on Surveying, prepared for the Press by the Rev. 
;Vbel Flint of Hartford ; and find it worthy of the pub- 
lic patronage. Every thing not immediately necessary 
for the practical Surveyor has been excluded ; while it 
comprises all which is requisite in Field Surveying, both 
on the old and new plan ; elucidated and explained with 
a degree of conciseness and perspicuity not usually to 
be found in Treatises on the same subject. The Ma- 
thematical Tables are reduced to less than half the size 
occupied by others ; and any inconvenience which 
might result from such reduction, is obviated by the in- 
sertion of a Table of Natural Sines, not usually found 
in works of this nature. The Surveyor who shall own 
this will not be under the necessity of purchasing Gib- 
son, which is a more expensive work. 

ASHER MILLER, Surveyor General. 
GEORGE GILLET, Deputy Surveyor 
for Tolland County. 

MiDPLETOWN, Oct, 3, 1804. 



PREFACE. 



The following work is chiefly a compilation from 
other Books ; and but very little new is added, ex- 
cept a more full explanation, than has yet been 
published, of Rectangular Surveying, or the 
method of calculating the Area of Fields arithmC' 
tically, without drawing a plot of them and mea- 
suring with a Scale and Dividers, as has been the 
common practice ; and also a more particular ex- 
planation of the use of Natural Sines than is con- 
tained in most Mathematical Books. 

The Compiler has endeavoured to render this 
work so easy and intelligible that a Learner will 
require but little assistance from an Instructer, ex- 
cept with regard to the construction and use of 
Mathematical and Surveying Instruments. Before, 
however, he enters on the study of this Book he 
must be well acquainted with common Arithmetiq, 
with Decimal Fractions, and the Square Root; 
and he must also know the various characters or 
marks used in Arithmetic. 

A Surveyor will doubtless find many questions 
arise in the course of his practice, for the solution 
of which, no particular directions are here given ; 
nor is it possible to give directions for every case 
that may occur. In all practical Sciences much 
must be left to the judgment of the practitioner, 
who, if he is well acquainted with the general 
principles of his Art, will readily learn to apply 
those principles to particular cases. 

The primary design of this treatise is to teach 
common Field Surveying ; at the same time it con- 
tains the elements of Surveyiiig upon a larger 



PREFACE. 

Stale ; and the system of Geometry and Trigone 
metry with which it is introduced, with the Prob- 
lems for the mensuration of Superficies, as also the 
Mathematical Tables at the end, will be found use- 
ftil for many other purposes. It would be well, 
therefore, for those who do not intend to become 
practical Surveyors to acquaint themselves with 
what is here taught ; and with this view the fdllow- 
ing work is very proper to be introduced into Aca- 
demies, and those higher Schools which are design- 
ed to fit young men for active business in life. In- 
deed every person who frequently buys and sells 
land should learn to calculate the Contents of a 
field arithmetically; a knowledge which maybe 
acquired in a very little time, from the particular 
explanation here given of that method. 

Notwithstanding the many Books already pub- 
lished on the subjects here treated upon, it was 
thought a work of this kind was really wanted, and 
that if judiciously executed it would be useful. It 
is more particularly necessary at the present time 
in Connecticut;, as the Legislature of the State 
have lately enacted a I ^aw on the subject of Sur- 
veying, in consequence of which more attention 
must be paid to the Theory of that Art than has 
been common. 

These considerations induced the Compiler to 
select from various publications what appeared to 
him important; and to arrange the wnole in a 
method best adaptejd, in his view, for teaching that 
useful Art. How far he has succeeded in his en- 
deavours to simplify the subject, and render it easy 
to the Learner, must be submitted to the test of 
experience. 

Hartford, Conn. October, 1804j- 



P PEEFACE. 

A GENERAL VIEW OF THE CONTENTS OP THIS WOBK. 

The System of Geometry is divided into two 
parts. The first contains Geometrical Definitions 
respecting Lines, Angles, Superficies, &c. The 
second part contains a number of Geometrical 
Problems necessary for Trigonometry and Survey- 
ing. 

The System of Trigonometry is also divided 
into two parts : and teaches the solution of ques- 
tions in Right and Oblique angled Trigonometry, 
by Logarithms and also by Natural Sines. 

The Treatise on Surveying is divided into three 
parts. Part first treats of measuring Land, and is 
divided into three Sections. The first contains 
several Problems respecting Mensuration, and for 
finding the Area of various Right-lined Figures 
and Circles. 

The second Section teaches different methods 
of taking the Survey of Fields ; also to protract 
them, and find their Area in the manner commonly 
practised, and likewise by Arithmetical and Tri- 
gonometrical calculations, without measuring Di- 
agonals and Perpendiculars with a Scale and Di- 
viders ; interspersed with sundry useful rules and 
directions. 

The thu'd Section is a particular explanation 
and demonstration of Rectangular Surveyings or 
the method of computing the Area of Fields from 
the Field Notes, by Mathematical Tables, without 
the necessity of plotting the Field. To this Sec- 
tion is added a useful Problem for ascertaining the 
true Area of a Field which has been measured by 
a Chain too long or too short. 



PRSPAtfi. 

Part second treats of laying out Land in various 
shapes. 

Part third contains sundry Problems and Rules 
for dividing Land and determining the true Course 
and Distance of dividing Lines, or from one part 
of a Field to another. To this is added an Appen- 
dix concerning the Variation of the Compass and 
Attraction of the Needle ; also, a rule to find the 
difference between the present Variation, and that 
at a time when a Tract was formerly surveyed, in 
order to trace or run out the original lines. 

The Mathematical Tables, are a Traverse Ta- 
ble, or Table of Difference of Latitude and De- 
parture, calculated for every Degree and quarter 
of a Degree, and for any distance up to 50 ; a Ta- 
ble of Natural Sines calculated for every Minute ; 
-a Table of Logarithms comprised in four pages, 
yet sufficiently extensive for common use ; and a 
Table of Logarithmic or Artificial Sines, Tangents, 
and Secants, calculated for every 5 Minutes of a 
Degree. To these Tables are prefixed particular 
explanations of the manner of using them. 



GEOMETRY. 



GEOMETRY is a Science which treats of the properties of 
Magnitude. 

PART I. 

Geometrical Definitions. 

1. A Point is a small Dot ; or, Mathematically considered, is 
that which has no parts, being of itself indivisible. 

2. A Line has length but no breadth. 

3. A Superficies or Surface, called also Area, has length and 
breadth, but no thickness. 

4. A Solid has length, breadth, and thickness. 

5. A Right Line is the shortest that can be drawn between 
two Points. 

Fis. \. 



G. The inclination of two Lines meeting 
one another, or the opening between them, 
is called an Angle. Thus at B. Fig. 1. is an 
Angle, formed by the meeting of the Lines 
AB and BC. 



1. If a right Line CD. Fig. 2. fijlupon an- 
other Right Line AB, so as to incline to nei- 
ther side, bat make the Angles on each side 
equal, then those Angles are called Right 
Angles ; and the Line CD is said to be Per- 
pendicular to the other Line. 

B 




10 



GEOMETRY 



Fin. S. 



8. An Obtuse Angle is greater than a Right 
Angle ; as ADE. Fig. 3. 

9, An Acute Angle is less than a Right 
Angle ; as EDB. Fig. 3. 





Fii 



Koie. When three letters are used to express an Angle, the 
roidtlle letter denotes the angular Point. 

10. A Circle is a round Figure, bounded 
by a Line equally distant from some Point, 
which is called the Centre. Fig. 4. 

11. The Circumference or Periphery of 
a Circle is the bounding Line ; as ADEB. 
Fig. 4. 

12. The Radius of a Circle is a Line 
drawn from the Centre to the Circumference ; 
as CB. Fig. 4. Therefore all Radii of the 
same Circle are equal. 

13. The Diameter of a Circle is a Right 
Line drawn from one side of the Circumfer- 
ence to the other, passing through the Centre ; 
and it divides the Circle into two equal parts, 
tailed Semicircles ; as AB or DE. Fig. 5. 

14. The Circumference of every Circle is 
supposed to be divided into 360 equal parts, 
called Degrees ; and each Degree into 60 
equal parts, called Minutes ; and each Minute 
into 60 equal parts, called Seconds 5 and these into Thirds, &c 

Note. Since ail Circles are divided into the same number of 
Degrees, a Degree is not to be accounted a quantity of any 
determinate length, as so many inches or feet, &c. but is- 
always to be reckoned as being the 360th part of the Cir- 
cumference of any Circle, without regarding the bigness- 
of the Circle. 




15. An Arch or Arc of a Circle is any part of the Circumfer- 
ence ; as BF or FD. Fig. 5 ; and is said to be an Arch of so 
many Degrees as it contains parts- of 360 into which the whoU 
Circle is divided. 



GEOMETRY 



11 



16. A Chord is a Right Line drawn from 
one end of au Arch to the other, and is the 
measure of the Arch ; as HG is the Chord of 
the Arch HIG. Fig, 6. 




Note. The Chord of an Arch of 60 degrees is equal in length 
to the Radius of the Circle of which the Arch is a part. 

3 7. The Segment of a Circle is a part of a Circle, cut off by 
1 Chord ; thus the space comprehended between the Arch HIG 
and the Chord HG is ■called a Segment. Fig. 6. 

18. A Quadrant is one quarter of a Circle ; as ACB. Fig. 6. 

19. A Sector of a Circle is a space contained between two 
Radii and an Arch less than a Semicircle; as BCD or ACD. 
Fig. 6. 

20. The Sine of an Arch is a Line drawn 
from one end of the Arch, perpendicular to 
the Radius or Diameter drawn through the 
other end ; Or, it is half the Chord of double 
the Arch ; thus HL is the Sine of the Arch 
HB. Fig. 7. 

21. The Sines on the same Diameter in- Af 
crease in length till they come to the Centre, 
iind so become the Radius. Hence it is plain 
that the Radius CD Fig. 7. is the greatest j. 
possible Sine, or Sineof 90 Degrees. 

22. The Versed Sine of an Arch is that part of (he Diameter 
or Radius which is between the Sine and the Circumference ; 
thus LB is the Versed Sine of the Arch HB. Fig. 7. 

23. The Tangent of an Arch is a Right Line touching the 
Circumference, and drawn perpendicular to the Diameter ; and 
is terminated by a Line drawn from the Centre through the 
other end of the Arch ; thus BK is the Tangent of the Arch 
BH. Fig. 7. 

JVote. The Tangent of an Arch of 45 Degrees is equal ic 
length to the Radius of the Circle of which the A-rch is a 
part. 




14. The Secant of ann Arch is a Line drawn fioaa the Cenii 



12 GEOMETRY. 

through one end of the Arch till it meets the Tangent ; thcfg 
CK is the Secant of the Arch BH. Fig. 7. 

26. The Complement of an Arch is what the Arch wants of 
90 Degrees, or a Quadrant ; thus HD is the Complement of the 
Arch BH. Fig. 7. 

26. The Supplement of an Arch is what the Arch wants 
of 180 Degrees, or a Semicircle ; thus ADHis the Supplement 
of the Arch BH. Fig. 1. 

27. The Sine, Tangent or Secant of the Complement of any 
Arch is called the Co-Sine, Co-Tangent, or Co-Secant of the 
Arch ; thus, FH is the Sine, DI the Tangent, and CI the Secant 
of the Arch DH ; or they are the Co-Sine, Co-Tangent, and Co- 
Secant of the Arch BH. Fig. 7. 

28. The measure of an Angle is the Arch of a Circle coij- 
tained between the two Lines which form the angle, the angular 
Point being the Centre ; thus', the Angle HCB. Fig.l. is mea- 
sured by the Arch BH : and is said to contain so many Degrees 
as the Arch does. 

JSfote. An Angle is esteemed greater or less according to the 
opening of the Lines which form it, or as the Arch inter- 
cepted by those Lines contains more or fewer Degrees. 
Hence it may be observed, that the bigness of an Angle 
does not depend at all upon the length of the including 
Lines; for all Arches described on the same Point, and 
intercepted by the same Right Lines, contain exactly the 
same number of Degrees, whether the Radius be longer or 
shorter. 

29. The Sine, Tangent, or Secant of an Arch is also the Sine, 
Tangent, or Secant of the Angle whose measure the Arch is. 

Fig. 8. ■ 

30. Parallel Lines are such as are equally A, '. B 

distant from each other ; as AB and CD. 

Fig. 8. C' 



31. A Triangle is a Figure bounded by 
Xhree Lines ; as ABC. Fig. 9. 

3?. An Equilateral Triangle has its three 
side? equal in length to each other. Fig. 9. 




GEOMETRY. 



1; 



Fig. 10. 



33. An Isocles Triangle has two of its sides 
equal, and the other longer or shorter. Fig. 10, 



34. A Scalene Triangle has three unequal 
sides. Fig. 11. 



35. A Right Angled Triangle has one 
Right Angle. Fig. 12. 




Fisr. 11. 




Fig. If 




Fis:. 13. 




36. An Obtuse Angled Triangle has one 
Obtuse Angle. Fig. 13. 



37. An Acute Angled Triangle has all its Angles Acute. 
Fig. 9, er 10. 

38. Acute and Obtuse Angled Triangles are called Oblique 
Angled Triangles, or simply Oblique Triangles ; in which the 
bottom Side is generally csdled the Base and the other two, 
Legs; 

39. In a Right Angled Triangle the longest side is called the 
Hypothenuse, and the other two, Legs, or Base and Perpen- 
dicular. 

JVote. The three Angles of every Triangle being added to- 
gether will amount to 180 Degrees ; consequently the two 
Acute Angles of a Right Angled Triangle amount to 90 
Degrees, the Rig;ht Angle being also 90. 
C 



u 



GEOMETRY. 



Fis;. 14 



40. The perpendicular height of a Trian- 
gle is a Line drawn from one of the Angles 
to its opposite side ; thus, the dotted Line 
ID. Fig. 14. is the perpendicular height of 
the Triangle ABC. B 




JYote. This Perpendicular may be drawn from either of thp 
Angles ; and whether it falls within the Triangle, or on 
one of the Lines continued beyond the Triangle, is imma- 
terial. 

Fig. 15. 



41. A Square is a Figure bounded by four 
equal sides, and containing four Right Angles. 

Ficr. 1.5. 



42. A Parallelogram, or Oblong Square, is 
a Figure bounded by four sides, the opposite 
ones being equal and the Angles Right. Fig. 
16. 



43. A Rhombus is a Figure bounded by 
four equal sides, but has its Angles Oblique. 
Fisc. 17. 




Fig. 16. 



Fig. 17. 



44. A Rhomboides is a Figure bound- 
d by four sides, the opposite ones being 
qual, but the Angles Oblique. Fig. 18. 




GEOMETRY. 13 

45. The perpendicular height of a Rhombus or Rhomboides 
is a Line drawn from one of the Angles to its opposite side : 
thus, the dotted Lines AB. Fig. 17. and Fig. 18. represent the 
perpendicular height of the Rhombus and Rhomboides. 

Fig. 19. 



* 46. A Trapezoid is a Figure bounded by 
four sides, two of which are parallel though 
of unequal lengths. Fig. 19. and Fig. 20. 



ZIZX 

Fig. 20. 




JVofe. Fig. 19. is sometimes called a Right Angled Trape 
zium. 



47. A Trapezium is a figure bounded by 
four unequal sides. Fig. 21. 

48. A Diagonal is a Line drawn between 
two opposite Angles ; as the Line AB. Fig. 
21. 

JC 

49. Figures w:hich consist of more than four sides are called 
Polygons ; if the sides are equal to each other they are called 
regular Polygons, and are sometimes named from the number 
of their sides, as Pentagon, or Hexagon, a Figure of five or six 
sides, &c. ; if the sides are unequal, they are called irregulat 
Polygons. 



PART II. 

Geometrical Problems. 

Fig. 22, ■ 
PROBLEM I. To draw a lAne parallel to ^ 

another Line at any given distance ; as at the >.-- . ^: - 

Point D, to make a Line, parallel to the Line ' 

AB. Fig. 22. A^ -n-r-' ^ 



16 GEOMETRY. 

With the Dividers take the nearest distance between the 
Point D and the given Line AB ; with that distance set one 
foot of the Dividers any where on the Line AB, as at E, and 
draw the Arch C ; through the Point D draw a Line so as just 
to touch the top of the Arch C. 

A more convenient way to draw parallel Lines is with ?i 
parallel Rule. 

Fig 23'. 



PROBLEM IL To bisect a given Line; .E 

to find the middle of it. Fii^. 23. ^ \ ^ 



■:1{T> 



Open the Dividers to any convenient distance, more than 
half the given Line AB, and with one foot in A, describe an 
Arch above and below the Line, as at C and D ; with the same 
distance, and one foot in B, describe Arches to cross the former : 
lay a Rule from C to D, and where the Rule crosses the Line. 
as at E, will be the middle. 



Fig. 24. 
H 



PROBLEM III. To erect a Perpendicular 
from the end, or any part of a given Line. Fig. 
24. 



> 






Open the Dividers to any convenient distance, as from D to 
A, and with one foot on the Point D. from which the Perpen- 
dicular is to be erected, describe an Arch, as AEG ; set off the 
same distance from A to E, and from E to G ; upon E and G 
describe two Arches to intersect each other at H ; draw a 
Line from H to D, and one Line will be perpendicular to the 
other. 

JVote. There are other methods of erecting a Perpendicular, 
but this is the most simple. 



GEOMETRY, 



ir 



PROBLEM IV. From a given Point, ^ 
as at (J, to drop a Perpendicular on a^ \^ 
s;iven Ldne AB. Fisr. 25. ^ F 



Fig. 25. 
C 



' Gr 



B 



With one foot of the dividers in C describe an Arch to cut 
the gfiven Line in two places, as at F and G ; upon F and G 
describe two Arches to intersect each other below the Line as 
at D ; lay a Rule from C to D and draw a Line from C to the 
given Line. 

Perpendiculars may be more readily raised and let fall, by a 
small Square made of brass, ivory, or wood. 

Fig. 26. 



PROBLEM V. To make an Angle at E,^^ 
equal to a given Angle ABC. Fig. 26. "''^^I 





Open the dividers to any convenient distance, and with one 
foot in B describe the Arch FG ; with the same distance and 
one foot in E, describe an Arch fromH ; measure the Arch FG, 
and lay off the same distance on the Arch from H to I ; draw 
a Line through I to E, and the Angles will be equal. 

Fig. 27. 




PROBLEM VL To maJce an Acute Angle 
fqual to a given nnmber of Degrees^ suppose 
36. Fig. 27. 



Draw the Line AB to any convenient length ; from a Scale 
of Chords take 60 Degrees with the dividers, and with one foot 
in B describe an Arch from the Line AB ; from the same Scale 
take the given number of Degrees, 36, and lay it on the Arch 
from C to D ; draw a line from B through D, and the Angle at 
B will be an Angle of 36 Degrees. 

D 



i8 



GEOMETRY. 



Kg-.' 28. 




PROBLEM VII. To malce an Obtuse An- 
gle, suppose of 110 Degrees, fig. 28. 



Take a Chord of 60 Degrees as before, and describe an Arch 
greater than a Quadrant ; set off 90 Degrees from B to C, and 
from C to E set off the excess above 90, which is 20 ; draw a 
Line from G through E, and the Angle will contain 110 De- 
grees. 

JYote. In a similar manner Angles may be measured ; that is^ 
with a Chord of 60 Degrees describe an Arch on the an- 
gular Point, and on a Scale of Chords measure the Arch 



intercepted by the Lines forming the angle. 



/ 



A more convenient method of making and measuring Angles 
is to use a Protractor instead of a Scale and Dividers. 

Fisr. 29. 



PROBLEM VIII. TomaheaTnangleoj 
Ihree given Lines, as BO, BL, LO. Fig. 29. 



Draw the Line BL from B to L ; from B, with the length ol 
the Line BO, describe an Arch as at ; from L, with the 
length of the Line LO, describe another Arch to intersect the 
former ; from draw the Lines OB and OL, and BOL will be 
the Triangle required. 

Fig. 30. 




PROBLEM IX. To make a Right Jingled 
Triangle, the Hypolhenuse and Angles being 
-7:iven, Fi^. 30. 



Sujipose the Hypothenuse CA 25 Rods or Chains, the angle 




GEOMETRY. 



id 



at C 35" 30' and consequently the Angle at A 54® 30'. Set 
JVote after the d9th Geometrical Definition. 

JVote. When degrees and minutes are expressed, they are 
distinguished from each other by a small cipher at the 
right hand of the degrees, and a dash at the right hand of 
the minutes ; thus 35° 30' is 35 degrees and 30 minutes. 

Draw the Line CB an indefinite length ; at C make an Angle 
of 35° 30' ; through where that number of Degrees cuts the 
Arch draw the Line CA 25 Rods, which must be taken from 
some Scale of equal parts ; drop a Perpendicular from A to B, 
and the Triangle will be completed. 

JVote. The length of the two Legs may be found by mea- 
suring them upon the same scale of equal parts from which 
the Hypothenuse was taken. 

Fi?. 31. 



PROBLEBI X. To make a Right An- 
gled Triangle, the Angles and one Leg being 
siven. Fior. 31. 



Suppose the Angle at C 33° 15', and the Leg AC 285. 

Draw the Leg AC making it in length 285 ; at A erect a Per- 
pendicular an indefinite length ; at C make an Angle of 33'^ 
15' ; through where that number of Degrees cuts the Arch, 
draw a Line till it meets the Perpendicular at B. 

JYote. If the given Line CA should not be so long as the 
Chord of 60°, it may be continued beyond A, for the pur- 
pose of making the Angle. 

Fis. 32. 



PROBLEM XL To make a Right Angled 
Triangle, the Hypothenuse and one Leg being 
"iven. Fis- 32. 





B 



A 2a 

Suppose the Hypothenuse AC 40, and the Leg AB 28. 
Draw the Leg AB in length 28 ; from B erect a Perpendi- 
cular an indefinite length ; take 40 in the Dividers, and setting 



20 



GEOMETRY. 




one foot in A, wherever the other foot strikes the Perpendicular 
will be the point C. 

JYote, When the Triangle is constructed, the Angles may be 
measured by a Protractor, or by a Scale of Chords. 

Fig. 33. 

C 



PROBLEM XII. To make a Right Angled 
Triangle, the two Legs being given. Fig. 33. 



Suppose the Leg AB 38, and the Leg BC 46. 
Draw the Leg AB in length 38 ; from B erect a Perpendicu- 
lar to C in length 46 ; and draw a Line from A to C. 

Fig. 34. 



PROBLEM Xm. To 

make an Oblique Jingled Tri- 
angle, the Jingles and one Side 
being given. Fig. 34. 



Suppose the side BC 98 ; the Angle at B 45o 15'', the Angle 
at D 108O 30^ consequently the other Angle 26° IS''. 

Draw the side BC in length 98; on the Point B make an An- 
gle of 450 15'' ; on the Point C make an Angle of 26° 15'', and 
draw the Lines BD and CD. 

Fis. 35. 



PROBLEM XIV. To make an Oblique 
Angled Triangle, two Sides and an Angle op- 
posite to one of them being given. Fig. 35. 





let? 



Suppose the side BC 160, the side BD 79, and the Angle at 
C 290 9^ 

Draw the side BC in length 160 ; at C make an Angle of 
290 9^, and draw an indefinite Line through where the Degrees 
cut the Arch ; take 79 in the dividers, and with one foot in B 
lay the other on the Line CD ; the point D will be the other 
Angle of the Triangle. 



GEOMETRY 



21 



D 



Fig. 36. 



PROBLEM XV. To make an Oblique'^ -^ 
Jingled Triangle, tivo Sides and their \^ — ^..N, 
contained Angle being given. Fig. 36. ^\%« 



i^e" 



aifp 



Suppose the side BC 109, the side BD 76, and the Angle at 
B lOlo 30'. 

Draw the side BC in length 109 ; at B make an Angle of 
101° 30', and draw the side BDin length 76 ; draw a line from 
D to C and it is done. 



Fis. 37. 



PROBLEM 

Wis. 37. 



XVL To make a Square. 




Draw the Line AB the length of the proposed Square ; from 
B erect a Perpendicular to C and make it of the same length as 
AB ; from A and C, with the same distance in the dividers, de- 
scribe Arches intersecting each other at D, and draw the Lines 
AD and DC. 



Fig. 38. 



PROBLEM XVIL To make a Parallelo- 

p-am. Fig. 38. 




Draw the Line AB equai to ta , longest side of the Parallelo- 
gram ; on B erect a Perpendicular the length of the shortest 
side to C ; from C, with the longest side, and from A, with the 
shortest side, describe Arches intersecting each other at D, and 
draw the Lines AD and CD. 



E 



GEOMETRY. 



:>%r 



PROBLEM XVIII. To desaibe 
a Circle tvhich ehall pass through 
any three given Points, not lying in ^ 
a Right lane, as A, B, D. Fig. 43. 



:j^ 



Fig. 43. 




Draw Lines from A to B and from B to D ; bisect those Lines 
by Problem II. and the Point where the bisecting Lines inter 
sect each other, as at C, will be the centre of the Circle. 

PROBLEM XIX. To find the centre of a Circle. 

By the last Problem it is plain, that if three Points be any 
where taken in the given Circle's Periphery, the centre of the 
Circle may be found as there taught. 

Directions for constructing irregular Figures of four or more 
sides pay be found in the following Treatise on Surveying. 



TRIGONOMETRY. 



TRIGONOMETRY is that part of practical Geometry by 
which the Sides and Angles of Triangles are measured ; where- 
by three things being given, either all sides, or sides and Angles. 
a fourth may be found ; either by measuring with a Scale and 
Dividers, according to the Problems in Geometry, or more 
accurately by calculation with Logarithms, or with Natural 
Sines. 

Trigonometry is divided into two Parts, Rectangular and 
Oblique-angular. 

PARTI. 

RECTANGULAR TRIGONOMETRY. 



This is founded on the following methods of applying a Tri- 
angle to a Circle. 

Fis. 44. 

PROPOSITION I. In every Right 
Angled Triangle, as ABC, Fig. 44, it is 
plain from Fig. 7. compared with the 
Geometrical definitions to which that 
Figure refers, that if the Hypothenuse A 
AC be made Radius, and with it an Arch \ 
of a Circle be described from each end, 
BC will be the Sine of the Angle at A, 
and AB the Sine of the Angle at C ; that 
is, the Legs will be Sines of their oppo- 
site Angles. 

PROPOSITION If. If one Leg, AB, 
Fig. 45, be made Radius, and with it on 
the Point A an Arch be described, then 
BC, the other Leg, will be the Tangent 
and AC the Secant of the Angle at A ; 
and if BC be made Radius, and. an Arch 
be described with it on the Point C, then 
AB will be the Tangent and AC the Se- 
cant of the Angle at C ; that is, if one Leg-^ 
be made Radius the other Leg will be a Tangent of its opposite 
Angle, and the Hypothenuse a Secant of the same Angle, 




U TRIGONOMETRY. 

Thus, as different sides are made Radius, the other sides ac- 
quire different names, which are either Sines, Tangents or Se- 
cants. 

As the sides and Angles of Triangles bear a certain propor- 
tion to each other, two sides and one Angle, or one side and 
two Angles being given, the other sides or Angles may be found 
by instituting Proportions, according to the following Rules. 

Rule I. To find a side, either of the sides may be made 
Radius, then institute the following Proportion : 

As the name of the side given, which will be either Radius, 

Sine, Tangent or Secant ; 
Is to the length of the side given ; 
So is the name of the side required, which also will be either 

Radius, Sine, Tangent or Secant ; 
To the length of the side required. 

Rule II. To find an Angle one of the given sides must be 
made Radius, then institute the following Proportion : 

As the length of the given side made Radius ; 

Is to its name, that is Radius ; 

So is the length of the other given side ; 

To its name, which will be either Sine, Tangent or Secant 

Having instituted the Proportion, look for the corresponding 
Logarithms, in the Logarithms for nimibers for the length of the 
sides, and in the Table of Artificial Sines, Tangents and Se- 
cants, for the Logarithmic Sine, Tangent or Secant. 

Having found the Logarithms of the three given Terms, add 
together the Log. of the second and third Terms, and from 
their sum subtract the Log. of the first Term, the Remainder 
will be the Log. of the fourth Term, which, seek in the Tables 
and find its corresponding Number or Degrees and Minutes. 

See the Introduction to the Table of Logarithms ; which 
should be attentively studied by the Learner before he proceeds 
any further. 

JVote. The Logarithm for Radius is always 10, which is the 
Logarithmic Sine of 90o, and the Logarithmic Tangent ol 
450. 

The preceding Propositions and Rules being duly attended 
to, the solution of the following Cases of Rectangular Tngono- 
metry will be easy. 



I 



TRIGONOMETRY 



Fig. 39. 



CASE I. 



2Vie Angles and Hypothenuse given to find 
the Legs. Fig. 39. 



In the Triangle ABC, given the Hypothenuse AC 25 Rods 
or Chains ^ the Angle at A 35° 30^ : and consequently the 
Angle at C 54° 30'' : to find the Legs. 

Making the Hypothenuse Radius, the Proportions. will be : 




To find the Leg AB. 
As Radius - - iD.OOOno 

r Hyp. AC, 25 - - 1.39784 

: : Sine ACB, 54° 30' 9.91069 



: Leff AB, 20.35 



1.30S63 



To find the Leg BC. 
As Radius - • 10.00000 

: Hyp. AC, 25 - - 1.39794 

: : Sine CAB, 35° 30' 9.76395 



: Leg BC, 14.52 



11.16189 
10.00000 



1.16189 



JVote. When the first Term is Radius, it may be subtracted 
by cancelling the first figure of the Sum of the other two 
Terms. 

Making the Leg AB Radius, the Proportions will be : 



To find the Leg AB. 
\s Secant CAB, 350 30^ 
Hyp. AC, 25 
: Radius 
Leg AB, 20.35 



To find the Leg BC. 
As Secant CAB, 35o 30' 
Hyp. AC, 25 
: Tangent, CAB, 35o 30' 
Leg BC, 14.52 



Making the Leg BC Radius, the Proportions will be 



To find the Leg AB. 
As Secant ABC, 540 30' 
Hyp. AC, 25 
: Tangent ACB, 54° 30^ 
Leg AB, 20.35 



To find the Leg BC. 
As Secant ACB, 54° 30' 
Hyp. AC, 25 
: Radius 
Leg. BC, 14.52 



The Logarithms of the four last Proportions being looked 
out, and added and subtracted according to the Rule, the result 
will be found to be the same as the two first Proportions. 

F 



ae TRIGONOMETRY 



By J^atural Sines. 

This Case may be solved by Natural Sines,* according to 
the following Proportions : 

As Unity or 1, is to the length ©f the Hypothenuse, so is the 
Natural Sine of the smallest Angle, to the length of the short- 
est Leg, Or, so is the Natural Sine of the largest Angle, to 
thfe length of the longest Leg. ' 

Or, which is the same thing, multiply the Natural Sines of 
the two Angles by the Hypothenuse, the Products will be the 
length of the two Legs. 

Example. 

Nat. Sine of 35° 30' Nat. Sine of 54° 30- 

0.58070 0.81412 

Hyp. 25 Hyp. 25 



290350 407060 

116140 162824 



14.51750 20.35300 



Leg BC 14.52 Leg AB 20.35 

JVote, The thiid Decimal figure in the first Product being 7, 
the preceding figure may be called one more than it is. 
viz. 2. And whenever in any Product, &c. there are more 
places of Decimals than you wish to work with, if the 
one at the right hand of the last which you wish to retain 
is more than 5, add a Unit to the last, because a greater 
_ number than 5 is more than half. 



As the Table of Artificial or Logarithmic Sines, Tangents | 
and Secants, contained in this book, is calculated only for every 
5 Minutes of a Degree, whenever any Question is to be solved 
where the Minutes cannot be found in that Table ; or where 
the length of the Hypothenuse is such a number as cannot be 
found in the Table of Logarithms for Numbers, the Question 
may be solved by Natural Sines as above taught. 

* See tlie Introduction to the Table of Natural Sines. 



I 






TRIGONOMETRY 



2:7 



CASE II. 



The Angles and one Leg given, to find the 
Hypothenuse and the other Leg, Fig. 40. 



Fi^, 40. 




325 



In the Triangle ABC, given the Leg AB 325, the Angle at A 
330 W and the Angle at C 56^ 45^ : to find the Hypothenuse 
and the Leg BC. 

Making the given Leg Radius, the Proportions will be : 



To find the Hypothenuse 
As Radius, 10.00000 

: Leg AB, 325 2.51188 

,: Sec. CAB, 33° 15' 10.07765 



Hyp. 388.6 



12.58953 



To find the Leg BC. 
As Radius, 10.00000 

: Leg AB, 325 2.511SS 

: : Tan. CAB, 33° 15' 9;81666 



LegBC, 213.1 



12,32854 



JVote. Reject the first figure, w^hich is the same as subtract- 
ing Radius, and seek the numbers corresponding to the 
other figures. 

Making the Leg BC Radius, the Proportions will be ; 



To find the Hypothenuse 
As Tang. ACB, 56° 45^ 
Leg AB, 325 
: Sect. ACB. 56° 45^ 
Hyp. 388.6 



To find the Leg BC, 
As Tang. ACB, 56° 45' 
Leg AB, 325 
: Radius 
LegBC, 213.1 



Making the Hypothenuse Radius, the Proportions will be ; 



To find the Hypothenuse. 
As Sme BCA, 560 45' 
Leg AB, 325 ' 
: Radius 
Hyp. 388.6 



To find the Leg BC. 
As Sine BCA, 56o 45' 
LegAB, 325 
: Sine BAC, 330 15' 
Leg BC, 213. 



Xote. If the Leg BC had been given, instead of the Leg AB, 
the Proportions would have been the same mutatis mutan^ 
dis. 



By Natural Sines. 

To solve this Case by Natural cSines, institute the following 
Proportions ; 



as TRIGONOMETRY. 

To find the Hypothmuse. As the Natural Sine of the Angle 
opposite the given Leg, is to the length of the Leg, so is Unity 
or 1, to the length of the Hypothenuse. 

Or, which is the same thing, Divide the given Leg by the 
Natural Sine of its opposite Angle^ and the Quotient will be 
the Hypothenuse. 

To find the other Leg. As the Natural Sine of the Angle op- 
posite the given Leg, is to the length of the given Leg, so is the 
Natural Sine of the Angle opposite the other Leg, to the length 
of the other Leg. 

Example. 

Given Leg 325. Nat. Sine of 56° 45'', the Angle opposite 
the given Leg 0.83629. Nat. Sine of 33° 15^, the Angle op- 
posite the other Leg 0.54829. 

As 0.83629 : 325 : : 1 : 388.6 

As 0.83629 : 325 : : 0.54829 : 213.07. 



CASE IIL 



The Hypothenuse and one Leg given, to find 
ike Angles and the other Leg. Fig. 41. 

" ^-4^ ^ 

In the Triangle ABC, given the Hypothenuse AC 50 and the 
Leg AB 40, to find the Angles and Leg BC. 

Making the Hypothenuse Radius, the Proportion to find. the 
Angle ACB will be : 

As Hyp. 50 - 1.69897 

: Radius - - 10.00000 

::LegAB, 40 - 1.60206 




11.60206 
1.69897 



Sine ACB, 53© 10' 9.90309 



The Angle ACB being 530 10^the other is consequently 
360 50^ 



TRIGONOMETRY. 29 

Making the Leg AB Radius, tke Angle BAC may be found by 
the following Proportion ; 

As Leg AB, 40 - 1.60206 

: Radius - - 10.00000 

: : Hyp. 50 - - 1.69897 

11.69897 
1.60206 



: Sec. BAC, 360 50^ 10.09691 
The Angles being found, the Leg BC may be found by either 
f the preceding Cases. It is 30. 



By J^atural Sines. 

The Angle opposite the given Leg may be found by the fol- 
lowing Proportion ; 

As' the Hypothenuse is to Unity or 1, so is the given leg to 
the Nat. Sine of its opposite Angle. 

Or, which is the same thing. Divide the given Leg by the 
Hypothenuse, and the Quotient will be the Nat. Sine. 

Example. 

The Leg AB 40 divided by the Hypothenuse 50 quotes 
0.80000 which looked in the Table of Nat. Sines, the nearest 
corresponding number of Degrees and Minutes will be found 
to be 53° 8^, the Angle ACB. 

JVote. The reason why the Angle as found by Nat. Sines 
differs 2 Minutes from the Angle as found by Logarithms, 
is that the Table of Logarithmic Sines, &c. contained in 
this book, is calculated only for every 5 minutes. By a 
Table of Logarithmic Sines, &c. calculated for every 
minute, the Angle will be found the same. 



J3y the Square Root. 

In this Case the required Leg may be found by the Square 
Root, without finding the Angles ; according to the following 
Proposition ; 

G 



30 TRIGONOMETRY. 

In every Right Angled Triangle, the Square of the Hypo= 
Ihenuse is equal to the Sum of the Squares of the two Legs. 
Hence, 

The Square of the given Leg being subtracted from the 
Square of the Hypothenuse, the Remainder will be the Square 
of the required Leg. 

As in the preceding Example ; the Square of the Leg AB 40 
is 1600 5 this subtracted from the Square of the Hypothenuse 
50 which is 2500, leaves 900, the Square of the Leg BC, the 
Square Root of which is 30, the length of Leg BC as found by 
Tjogarithmg; 



CASE lY- 

Fk. 42. 



Tlie Legs given to find the Angles and Hij- 




foilunuse. Fig. 42 



in the Triangle ABC, given the Leg AB 78.7 and the Leg 
BC 89 ; to find the Angles and Hypothenuse. 

Making the Leg AB Radius, the Proportion to find the Angk 
BAG will be ; 

As Leg AB, 78.7 1.89597 

: Radius - « 10.00000 
; : Leg BC, 89 - 1.94939 



11.94939 
1.89597 



Tang. BAC, 480 30^ 10.05342 



The Angle ACB is consequently 41© 30'. 

Making the Leg BC Radius, the Proportion to find the Angle 
EGA will be the same as the above, mutatis mutandis. 

The Angles being found, the Hypothenuse may be found bv. 
CaseIL It is nearest II 9o 



TRIGONOMETRY . 31 

By the Square Root, 

In this Case the Hypothenuse may be found by the Square 
Root, without finding the Angles ; according to the following 
Proposition. 

In every Right Angled Triangle, the sum of the Squares of 
the two Legs is equal to the Square of the Hypothenuse. 

In the above Example, the Square of AB 78.7 is 6193.693 
the Square of BC 89 is 7921 ; these added make 14114.69 the 
Square Root of which is nearest 119. 



Sy JVatural Sines. 

The Hypothenuse being found by the Square Root, the Angles 
may be found by Nat. Sines, according to the preceding Case, 
Hyp, Leg. BC. Nat. Sine, 
119) 89.00000 (74789 
83 3 ... . 



570 The nearest degrees and minutes cor- 

476 responding to the above Nat. Sine are 48^ 

= 24^ for the Angle BAC. The difference 

940 between this and the Angle as found by 

833 Logarithms is occasioned by dividing by 

119, which is not the exact length of the 

1 070 Hypothenuse, it being a Fraction too much . 
962 



1180 
1071 

109 



PART IL 

Oblique Trigonometry. 

The solution of the two first Cases of Oblique Trigonometi.'y 
depends on the following Proposition. 

In all Plane Triangles, the Sides are in proportion to each 
other as the Sines of their opposite Angles. That is, as the 



33 TRIGONOMETRY. 

Sine of one Angle is to its opposite Side, so is the Sine of an- " 
other Angle to its opposite Side. Or, as one Side is to its oppo- 
site Angle, so is another Side to the Sine of its opposite Angle* 

Note. When an Angle exceeds 90° make use of its Supple- 
ment, which is what it wants of 180^. As the Sine of 90° 
is the greatest possible Sine, the Sine of any number of 
Degrees will be as much less as that number of Degrees 
exceeds 90, and will be the same as the Sine of the Sup- 
plement of that number of Degrees ; thus, the Sine of 
lOOo is the same as the Sine of SQo, and the Sine of 130C^- 
the same as the Sine of 50o, &c. 



CASE L 



The Jingles and one Side given, to find the 
dker Sides, Fis;. 47. 




2(^0 



In the Triangle ABC, given the Angle at B 48°, the Angle 
at G 72°, consequently the Angle at A 60°, and the Side AB 
200, to find the Sides AC and BC. 



To find the Side AC. 
As Sine ACB, 72' - 9.97821 
: Side AB, 200 - - 2.30103 
: : Sine ABC, 43° - 8.87107 



Side AC, 156 



12.17210 
9.97821 



2.19389 



To find the Side BC. 
As Sine ACB, 73"=" - 9.97821 , 
: Side AB, 200 - - 2.30103 » 
: : Sine BAC, 60° - 9.93753 1 



Side BC, 182 



12.32856 
9.97821 



2.26033 



By JSTatural Sines. 

As the Nat. Sine of the Angle opposite the given Side is^^to 
the given Side, so is the Nat. Sine of the Angle opposite either 
of the required Sides to that required Side. 



TRIGONOMETRY. 



3$ 



Given Side 200 ; Nat. Sine of 72°, its opposite Angle, 
0.95115 ; Nat. Sine of ABC 48©, 0.74334; Nat. Sine ofBAC 
60O, 0.86617. 

As 0.95115 : 200 : : 0.74334 : 156 

As 0.95115 : 200 : : 0.86617 : 182. 



CASE II. 



Two Sides, and an Angle opposite to one of 
Ihem given, to find the other Angles and Side. 
AV. 48. 



In the Triangle ABC, given the Side AB 240, the Side BC 
■200, and the Angle at A 46° 30' ; to find the other Angles and 
the Side AC. 

To find the ^iigle ACS. | 

As Side BC, 200 2.30103 

: Sine BAG, 46° 30' g.SeO.'io 

:: Side AB, 240 2.38021 




12.24077 
2.30103 



9.93974 



Angle at A 
C 


46° 30' 
60 30 




107.00 


Sum of the three Angles 
Sum of two 


XSO" 
107 



Sine ACB, 60° 30' 

■ I Angle at B 73 

The Side AC will be found by Case I. to be nearest 253. 

JVbfe. If the given Angle be Obtuse, the Angle sought will 
be Acute ; but if the given Angle be Acute, and opposite 
a given lesser Side, then the Angle found by the operation 
may be either Obtuse or Acute. It ought therefore to be 
mentioned which it is, by the conditions of the question^ 



By Matural Sines^. 

As the Side opposite the given Angle is to the Nat. Sine of 
that Angle, so is the other given Side to the Nat. Sine of its 
opposite Angle. 

One given Side 200, Nat. Sine of 46^ 30'', its opposite Angle. 
0.72537, the other given Side 240. 

As 200 : 0.72537 : : 240 : 0.87044=600 30". 

H 



u. 



TRIGONOMETRY 



CASE III. 



2\vo Sides and their contained Angle given, 
f.o find the other Angles and Side. Fig. 49. 




9^0 



The solution of this Case depends on the following Propo- 
sition. 

In every Plane Triangle, as the sum of any two Sides is to 
their difference, so is the Tangent of half the sum of the two 
opposite Angles to the Tangent of half the difference between 
them. Add this half difference to half the sum of the Angles 
and you will have the greater Angle, and subtract the half dif- 
ference from the half sum and you will have the lesser Angle. 

In the Triangle ABC, given the Side AB 240, the Side AC 
180, and the Angle at A 36° 40^ to find the other Angles and. 
Side. 

SideAB - 240 Al. - 240 

AC - 180 AC - 180. 



Sum of the two Sides 420 



Difference 



60 



The given Angle BAC 36° 40^, subtracted from 180°, leaves 
143° 20^ the sum of the other two Angles, the half of which is 

'no 40^ 

As the sum of two Sides, 420 - - 2.62325 

: Their difference 60 ... 1.77815 

: Tangent half unknown Ang. 71° 40' - 10.47969 



: Tangent half difference, 230 20 

The half sum of the two unknown Angles, 
The half difference between them. 

Add, gives the greater Angle ACB 

Subtract, gives the lesser Angle ABC 

The Side BC may be found by Case I or II, 



12.25784 
2.62325 

9.63459 

710 40 
23 20 

95 00 

48 20 



TRIGONOMETRY. 



Fig. 50. 




CASE IV. 



T'he three Sides given to find the An- 
gles. Fig. 50. 



A. i05 » B 

The solution of this Case depends Ofi the following Propo- 
sition. 

In every Plane Triangle, as the longest Side is to the sum 
of the other two Sides, so is the difference between those two 
Sides to the difference between the Segments of the longest 
Side, made by a Perpendicular let fall from the Angle opposite 
that Side. 

Half the difference between these Segments, added to half 
the sum of the Segments, that is, to half the length of the 
longest Side, will give the greatest Segment; and this half dif- 
ference subtracted from the half sum will be the lesser Seg- 
ment. The Triangle being thus divided, becomes two Right 
Angled Triangles, in which the Hypothenuse and one Leg are 
given to find the Angles. 

In the Triangle ABC, given the Side AB 105, the Side AC 
S5, and the Side BC 50, to find the Angles. 

Side AC - 85 AC - - 85- 

BC - 50 BC = - 50 



Sum of the two Sides 135 



Difference 



35 



As the longest Side AB, 105 
Sum of the other two Sides, 135 
: Difference between those Sides. 



35 



Difference between the Segments, 45 

Half the Side AB 

Half the difference of the Segments 

Add, gives the greater Segment AD 

Subtract, gives the lesser Segment BD 



2.02119 
2.13033 
1. 54407 

3.67440 
2.02119 

1.65321 



3e 



TRIGONOMETRY. 



Thus the Triangle is divided into two Right Angled Trian- 
gles, ADC and BDC ; in each of which the Hypothenuse and 
one Leg are given to find the Angles. 



To find the Angle DCA. 
As Hyp. AC, 85 - 1.92942 

: Radius ... 10.00000 
; : Seg. AD, 75 - . 1.87506 



11.87506 
1.92942 



Sine DCA, 61° 55' 



9.94564 



To find the Jingle DCB. 
As Hyp. BC, 50 - 1.69897 

: Radius - . . 10.00000 
: : Seg. BD, 30 - - 1.47712 



: Sine DCB, 36° 50' 



11.47712 
1.69897 



9.77815 



The Angle DCA 61© 55^ suhtracted from 90O leaves the 
Angle CAD 28o 5^ 

The Angle DCB 36° 50'' subtracted from 90° leaves the An- 
gle CBD 530 10^. 

The Angle DCA 61© 55^ added to the Angle DCB 360 50^ 
gives the Angle i\CB 98© 45''. 

This Case maj' also be solved according to the following 
Proposition^ 

In every Plane Triangle, as the Product of any two Sides 
containing a required Angle is to the Product of half the sum 
of the three Sides, and the difference between that half sum 
and the Side opposite the Angle required, so is the Square of 
Radius to the Square of the Co-Sine of half the Angle re-, 
quired. 



Those who make themselves well acquainted with Trigono- 
metry will find its application easy to many useful purposes, 
particularly to the mensuration of Heights and Distances ; 
called Altimetry and Longimetry. These are here omitted, 
because, as this work is designed principally to teach the Art 
of common Field-Surveying, it was thought improper to swell 
its size, and consequently increase its price, by inserting any 
thing not particularly connected with that Art. 

It is recommended to those who design to be Surveyors to 
stVv*3y Trigonometry thoroughly ; for though a common field 
may be measured without an acquaintance with that Science, 
yet many cases will occur in practice where a knowledge of it 
will be found very beneficial ; particularly in dividing Land, 
and ascertaining the boundaries of old Surveys. Indeed no 
one who is ignorant of Trigonometry, can be an accomplished 
Surveyor. 



SURVEYING. 



SURVEYING is the Art of measuring, laying out, and di- 
viding Land. 

PART I. 

Measuring Land. 

The most common measure for Land is the Acre ; which 
contains 160 Square Rods, Poles or Perches ; or 4 Square 
Roods, each containing 40 Square Rods. 

The instrument most in use, for measuring the Sides of Fields, 
is Gunter's Chain, which is in length 4 Rods or 66 Feet ; and 
is divided into 100 equal parts, called Links, each containing 7 
Inches and 92 Hundredths. Consequently, 1 Square Chain 
contains 16 Square Rods, and 10 Square Chains make 1 Acre. 

In small Fields, or where the Land is uneven, as is the case 
with a great part of the I^and in New-England, it is better to 
use a Chain of only two Rods in length ; as the Survey can be 
more accurately taken. 



SECTION I. 

Preliminary Problems. 

PROBLEM I. To reduce Ttvo Rod Chains to Four Ro<^ 
Chains, 

Rule. If the number of Two Rod Chains be even, take 
half the number for Four Rod Chains, and annex the Links if 
any : thus, 16 Two Rod Chains and 37 Links make 8 Four 
Rod Chains and 37 Links. 

But if the number of Chains be odd, take half the greatest 
even number for Chains, and for the remaining number add 50 
to the Links : Thus, 17 Two Rod Chains and 42 Links m^e 
8 Four Rod Chains and 92 Links. 

PROBLEM II. To reduce Tioo Rod Chains to Rods and 
DecinMl Parts. 

I 



38 SURVEYING. 

Rule. Multiply the Chains by 2, and the Links by 4, vvhiclt 
will give Hundredths of a Rod : thus, 17 Two Rod Chains and 
21 Links make 34 Rods and 84 Hundredths ; expressed thus, 
34.84 Rods. 

If the Links exceed 25, add 1 to the number of Rods and 
multiply the excess by 4 : thus, 16 Two Rod Chains and 38 
Links make 31.52 Rods. * 

PROBLEM HI. To reduce Four Rod Chains to Rods mnd 
Decimal parts. 

Rule. Multiply the Chains, or Chains and Links, by 4 ; 
the Product will be Rods and Hundredths : thus, 8 Chains and 
64 Links make 34.56 Rods. 

^Xote. The reverse of this Rule, that is, dividing by 4, will reduce Rods 
and Decimals to Chains and Links : thus, 105.12 Rods make 26 Chains 
and 2S Links. 

PROBLEM IV. To reduce Square Rods to Acres. 

RcLE. Divide the Rods by 160, and the Remainder by 40, 
if it exceeds that number, for Roods or Quarters of an Acre : 
thus, 746 Square Reds make 4 Acres, 2 Roods, and 26 Rods. 

PROBLEM V. To reduce Square Chains to .Aa-es. 

Rule. Divide by 10 ; or, which is the same thing, cut off' 
the Right hand figure : thus, 1460 Square Chains make 146 
Acres ; and 846 Square Chains make 84 Acres and 6 Tenths. 

PROBLEM VI. 2 reduce Square Links to Acres. 

Hulk. Divide by 100000 : or, which is the same thing, cut 
off' the 5 Right-hand figures : thus, 3845120 Square Linksmakc 
38 Acres and 45120 Decimals. 

J\^ole. When the Area of a Field, by which is meant its Superficial Con- 
tents, is expressed in Square Chains and Links, the whole may be consi- 
dered as Square Links, and the number of Acres contained in the Field, 
found as above. Then multiply the figures cut ofi" by 4, and again cut 
cfi" 5 figures, and you have the Roods ; multiply the figures last cut oft" 
by 40, and again cut off 5 figures, and you have the Rods. 

Example. How many Acres, Roods, and Rods, are there in 15Cs 
Sqaare Chains a,nd 3274 Square Links ? 

15)63274 Square Links, 
4 



2)53096 
40 

21)23840 



Jinsiaer. 15 Acres 2 Roods and 21 Rods. 



Problems for finding the Area of Right Lined Figures, and 
also of Circles. 



SURVEYING. 39 

PROBLEM Vll. To find ihe .^ea of a Square or ParaU 
Idogram. 

Rule. Multiply the length into the breadth ; the Product 
will be the Area. 

PROBLEM VIIL To find the Area of a Rhombm or 
Shomboides. 

Rule. Drop a Perpendicular from one of the Angles to its. 
opposite Side, and multiply that Side into the Perpendicular; 
the Product will be the Area. 
:r PROBLEM IX. To find the Area of a Triangle^ 

Rule 1. Drop a Pei-pendicular from one of the Angles to its 
opposite Side, which may be called the Base ; then multiply 
the Base by half the Perpendicular, or the Perpendicular by 
half the Base ; the Product will be the Area. Or, multiply the 
whole Base by the whole Perpendicular, and half the Product 
will be the Area. 

Rule 2. If it be a Right Angled Triangle, multiply one of 
the Legs into half the other; the Product will be the Area. 
Or, multiply the two Legs into each other, and half the Pro- 
duct will be the Area. 

Rule 3. When the three Sides of a Triangle are known, the 
Area may be found Arithmetically, as follows : 

Add together the three Sides ; from half their Sum subtract 
each side, noting down the Remainders ; multiply the half Sum 
by one of those Remainders, and that Product by another Re- 
mainder, and that Product by the other Remainder ; the Square 
Root of the last Product will be the Area. 

Example. Suppose a Triangle whose three Sides are 24, 
20, and 18 Chains. Demanded the Area. 

24+20 + 18=62, the Sum of the three Sides, the half of 
which is 31. From 31 subtract 24, 20^ and 18 ; the three Re- 
mainders will be 7, 11, and 13. 

31X7=217; 217X11=2387; 2387x13=31031, the 
Square Root of which is 176.1, or 17 Acres 2 Roods and IT 
Rods. 

By Logarithms, 

As the Addition of Logarithms is the same as the Multipli- 
cation of their corresponding Numbers ; and as the Number 
answering to the one half of a Logarithm will be the Square 
Root of the Number corresponding to that Logarithm : it fol* 
lows. That if the Logarithm of the half Sum of the three Sides 
an,d the Logarithms of the three Remainders be added together. 



40 



SURVEYING. 



the Number corresponding to one half the Sum of those Lpg- 

arithnas will be the Area of the Triangle. 

The half Sum, 31 - - - 1.49136 

The first Remainder, 7 - - - 0.84510 

The second Remainder, 11 - - 1.04139 

The third Remainder, 13 - - 1.11394 



The Square of the Area, 31000 - 
Area 176 Square Chains 



4.49179 



2.24589 



Rule 4. When two Sides of a Triangle and their contained 
Angle, that is, the Angle made by those Sides, are given, the 
Area may be found as iollqws : 

Add together the Logarithms of the two Sides ^nd the Lo- 
garithmic Sine of the Angle ; from their sum subtrafct the Lo- 
garithm of Radius, the Remainder will be the Logarithm of 
double the Area. 

Example. Suppose a Triangle one of whose Sides is 105 
Rods and another 85, and the Angle contained between them 
28^5^. Demanded the Area. 

One Side, 105 .... 2.02119 

The other Side, 85 r - - 1.92942 

Sine Angle, 28° 5' - - - - 9.67280 



Subtract Radius 
Double Area, 4200 Rods 
Msiver. 2100 Rods. 



13.62341 
10.00000 

3.62341 



A^ete. Radius^may be subtracted by cancelling tlie Left-band figure of tlie 
Index, or subtracting 10, withoiit the trouble of setting down the Ci- 
phers. 



By J^atural Sines, 

Multiply the two given Sides into each other, and that Pro- 
duct by the Natural Sine of the given Angle ; the last Product 
will be double the Area of the Triangle. 

Nat. Sine of the Angle 28° 5' 0.47076 

105 X 85=8925, and 8925 X 0.47076=4201 the double Area 
of the Triangle. 

PROBLEM X, Te find the Area of a Trapezoid'. 



SURVEYING. 41 

KuLE. Multiply half the Sum of the two parallel Sides by 
the perpendicular distance between them, or the sum of the 
two parallel Sides by half the perpendicular distance, the pro- 
duct will be the Area. 

PROBIiEM XI. To find the Area of a Drapeziiim, or irre- 
gular Four Sided Figure. 

Rule. Draw a Diagonal between two opposite Angles, which 
will divide the Trapezium into two Triangles. Find the Area 
of each Triangle and add them together. Or, multiply the 
Diagonal by half the Sum of the two perpendiculars let fall 
upon it, or the Sum of the two perpendiculars by half the Dia- 
gonal, the product will be the Area. 

A'ofe. HTiere the length of the four Sides and of tj^e Diagonal is known, 
the Area of the two Triangles, into which the Trapezium is divided, 
may be calculated Arithmetically, according to Prob. IX. Rule 3. 

PROBLEM XII. To find the Area of a Figure containing 
more than Four Sides. 

Rule. Divide the Figure into Triangles, and Trapezia, by 
drawing as many Diagonals as are necessary, which Diagonals 
must be so drawn as not to intersect each other ; then find the 
Area of each of the several Triangles or Trapezia, and add 
them together ; the sum will be the Area of the whole Figure. 

J\^ote. A little practice will suggest the most convenient way of drawing 
the Diagonals ; but whichever way they are drawn, provided they do. 
not intersect each other, the whole Area will be found the same. 

PROBLEM XIII. Respecting Circles. 

Rule 1. If the Diameter be given the Circumference may 
be found by one of the following proportions : as 7 is to 22, or 
more exactly, as 113 is to 355, or in Decimals, as 1 is to 3. 14159, 
so is the Diameter to the Circumference. 

Rule 2. If the Circumference be given the Diameter may 
be found by one ot the following proportions : as 22 is to 7, or 
as 355 is to 113, or as 1 is to 0.31831, so is the Circumference 
to the Diameter. 

Rule 3. The Diameter and Circumference being known, 
multiply half the one into half the other, and the product will 
be the Area. 

Rule 4. From the Diameter only, to find the Area : multi- 
ply the Square of the Diameter by 0.7854, and the product will 
be the Area. 

Rule 5. From the Circumference only to find the Area ; 

K 



42 



SURVEYING. 



multiply the Square of the Circumference by 0.07958, and the 
product will be the Area. 

Rule 6. The Area being given to find the Diameter : divide 
the Area by 0.7854, and the Quotient will be the Square of the 
Diameter ; from this extract the Square Root, and you will 
have the Diameter. 

Rule 7, The Area being given to find the Circumference v. 
divide the Area by 0.07958, and the quotient will be the Square 
of the Circumference ; from this extract the Square Root, and 
Tou will have the Circumference. 



SECTION II. 

The following Cases teach the most usual methods of taking 
the Survey of Fields ; also, how to protract or draw a Plot oi' 
them, and to calculate their Area. 

JVbfe. The Field Book is a Register containing the length of the Sides 
of a Field, as found by measuring them with a Chain ; also the Bear- 
ings or Courses of the Sides, or the Quantity of the several Angles, a? 
found by a Compass or other instrument for that purpose ; together with 
such Remarks as the Surveyor thinks proper to make in the Field. 



CASE I. 



To survey a Triangular Field. 

Measure the Sides of the Field with a Chain, and enter their 
several lengths in a Field Book, protract the Field on Paper, 
and then find the Area by Prob. IX. Rule 1 . Or, without plot- 
'«ng the Field, calculate the Area by Prob. IX. Rule 3. 

Fig. 46=. 
FIE-LD BOOK. See Fig. 46. 
Chains. 
AB - - 20 

BC - - 24 

CA - - 18 

To -find the Jlrea. 

Ch. L. 
BaseBC - - 24.00 
HalfPerp. AD - 7.34 

9600 




SURVEYING; 

960Q 
7200 
16800 



Acres 17)61600 
4 

Roods 2) 46400 
40 



Rods 18) 56000 



Acres Roods Rods 
Area 17 — 2 — 18.56 
JVoie. When there are ciphers at the Right Hand of the Links, they 
may be rejected ; remembering to cut off a proper number of figures 
according to Decimal Rules. 

Observe, That in measuring witli a Chain, slant or inclined 
Surfaces, as the Sides of Hills, should be measured horizontally, 
and not on the Plane or Surface of the Hill ; otherwise, a sur- 
vey cannot be accurately taken. To effect this, the lower end 
of the Chain must be raised from the ground, so as to have the 
whole in a horizontal Line ; and the end thus raised must be 
directly over the Point where the Chain begins or ends, accord- 
ing as you are ascending or descending a Hill ; which Point may 
be ascertained by a Plummet and Line. 



CASE iL 

To suroey a Field in the form of a Trapezium,. 

Measure the several sides, and a Diagonal between two op- 
posite Angles ; protract the Field, and find the Area by Proe- 
tEM XI. Or, without protracting the Field, calculate the Area 
according to the JYote at the end of that Problem. 

Fig. 51, 



FIELD BOOK. 


See Fig. 51. 1-. 






Ch. h. 


AB 


~ 


27.50 


BC 


~ 


11.70 <v/ 


CD 


. 


21.50 W 


DA 


_ 


14.70 7 


J^agonalAQ 


- 


2S. p' 



9^ 50 



—^B 



44 



SURVEYING. 



To protract ihia Trapezium. 
Draw the Side AB the given length ; with the Diagonal A(J 
28 and the Side BC 11.70 describe cross Arches as at C, from 
A and B as Centres ; and the point of intersection will represent 
that corner of the Field : then, with the Side CD 21.50 and the 
Side AD 14.70, describe cross Arches as at D, from A and C_^ as 
Centres ; and the point of intersection will represent that cor- 
ner of the field. 



To find the £.rea. 



Perpendicular B a 
— Dm 



Half Diagonal AC 



22.44 
14.00 

897600 
2244 

Acres 31)416 

4 



Rood 1)664 
40 



Rods 26)560 
Acres Rood Roda 
Area 31 — 1 — 26.56 

JVbte. The Perpendiculars need not be actually drawn ; their length may 
be obtained as follows : From the Angle opposite the Diagonal open the 
Dividers so as when one Foot is in the angular Point, as at B, the other, 
being moved backwards and forwards, may just touch the Diagonal at a, 
and netther go the least above or below it ; that distance in the Dividers 
being measured on the Scale will give the length ef the Perpendicular. 



CASE ITI. 



To suri^ey a Field ivhich has more than four Sides, by the Chain 
only. 

Measure the several Sides, and from some one of the Angles, 
irOm which the others may be seen, measure Diagonals to 



SURVEYING. 



45 



them ; draw a Plot of the Field, and find the Area by Prob- 
lem XII. 



FIELD BOOK. See Fig;. 52. 



Fig. 52. 



••■•11 




30 6P 



AB 
BC 
CD 
DE 
EF 
FA 



Ch. L. 




30.60 




20.40 




22.40 


AC 


16.20 


AC 


13.50 


AE 


28. 





Diagonals. 



Ch. L. 
45. 
35. 
24.20 



To protract this Field, 
Draw the side AB, making it the given length 30.60 ; with 
the Diagonal AC 45 and the Side BC 20.40, describe cross 
Arches as at C, fi'om the Points A and B as Centres, and the 
Point of intersection will represent that Corner of the Field : 
draw the Side BC and the dotted Diagonal AC ; with the Dia- 
gonal AD 35 and the Side CD 22.40, describe cross Arches as 
at D, from the Points A and C, and draw the Side CD and the 
dotted Diagonal AD. Proceed in this manner till all the Sides 
and Diagonals are drawn. 



To find the Area. 

The Field, being plotted, may be divided into one Trapezium 
and two Triangles ; the Area of which is • calculated as fol- 
lows : — 

L 



46. 



SURVEYING. 



The Trapezium ABCD. 



Perpend, B a 
— Do 



Half Diag. AC 



Square Chains 



143900 
5756 
5756 



647.5500 



The Triangh AVE. 
Perpend. En 
Half Side AF 



Square Chains 

Acres Roods Rods 
,/Jrea 98 — — 34.4 



The Triangle ADE. 
HalfPerp. Em 
Diag. AD ... 



11.65 
14 

4660 
1165 



163.10 



Square Chains 



Trap. ABCD 
Triangle ADE 
Triangle AFE 



4.90P 
3f5- 

245d 
1470 

-- 171.50 



647.55. 
171.50 
163,10 



Acres 98)215 
4 

Roods .860 
40 

Rods 34)400, 



REMARKS. 



As each of the Sides of the several Triangles, into which the 
preceding Plot of a Field is divided, is known from the Field 
Book, the Area of the Field may be calculated Arithmetically, by 
finding the Area of each Triangle, according to Prob, IX. Rule 
3 ; and then adding the whole together. This method, though 
it may require more time, is preferable to the other, because 
more accurate. Indeed it is always better to calculate the' Area 
of a Field Arithmetically than Geometrically ; for in the former 
no two persons can differ in their calculations ; whereas, ac- 
cording to the latter, which is the common method of casting 
the contents of a Field, it is hardly to be expected that any two 
persons will perfectly agree. The inaccuracy of Scales, and 
the difficulty of determining with precision the length of Sides 
and Perpendiculars with a Scale-and Dividers, render it almost 
if not quite impossible to obtain the exact Area of a Field, in 
the method commonly practised, even if the Surveyor has mea- 
sured it accurately in the fii;st place. 

Other methods of taking the Survey of a Field by the Chain, 
only are mentioned in some Treatises on this subject, but they 



SURVEYING. it 

are rather curious than useful ; and it is much better to ascer- 
tain the Angles by an accurate Compass, or some instrument 
designed purposely for taking Angles. 



CASE IV. 

To Survey a Field with a Chain and Compass. 

Measure the length of the Sides with a Chain, and take their 
bearing or Course with a Compass ;* enter these in a Field 
Book ; plot the Field on paper, and calculate the Area by the 
directions already given. 

To protract or draio a.J\Iap of a Field, 

' Draw a Line to represent a Meridian, or North and South 
Line, from which lay off a Bearing or Course of the first Side 
of the Field j with a Protractor or Irom a Line of Chords ; and 
from a Scale of equal parts, measure the length of the Side and 
draw a Line to represent it. 

At the end of this Line draw a Line parallel to the Meridian 
Line, and then lay off the second Side of the Field as before 
taught ; proceed in the same manner to draw parallel Lines, 
and lay off the several Sides till the whole is protracted. 

In protracting a Field, let the top of the paper be considered 
as North, the bottom South, the right hjij^d Etiot, and ibe left 
hand West ; lay the Course to the right or left of the Meridian. 
Line, according as it is East or West, and from the upper or 
lower part of the Line, according as it is North or South. 

In all protractions, if the end of the last distance falls exactly 
on the point from which you began, the Course also being right,. 
the Field work and protraction are truly taken and performed ; 
if not, an error must have been committed in one of them : in 
such cases, make a second protraction ; if this agrees with the 
former, it is to be presumed the fault is in the Field work ; a 
re-survey must then be taken. 

* A Compass may be so constructed with two Indexes, one moveable and 
the other fixed, as to ascertain the Angle made by two Sides, without refer- 
ence to the Bearing of those Sides. Such a Compass would be particularly 
useful in surveying Land where there are mineral substances which have an 
influence upon the Compass Needle, attracting it one way or the other, S,nd 
thus rendering it impossible to tafee a Conrse by it with precision. 



4B 



SURVEYING. 



Example I. 



FIELD BOOK. See Fig. 53. 
Ch. L. 



Fi!{. 53, 



AB. N. 70 0' . W. 


28.20 


BC. N. 74 E. 


39.50 


CD. S. 9 E. 


38. 


DE. N. 63 20 W. 


14.55 


EA. S. 74 W. 


28.60 


Acres Rood Rods 


Area 117 — 1 — 6 






REMARKS. 



The Sides of the several Triangles into" which the Plot of a.. 
Field is divided may be found by Trigonometry ; and then the 
Area of each Triangle may be calculated according to Prob. 
IX. Rule 3. The Sum of the Areas of the several Triangles 
will be the Area of the whole Field. This method may require 
more time, but it is perfectly accurate, since no dependence is 
placed on the uncertain measurement of Scale and Dividers. 

In the preceding Example, suppose the Field divided into 
three Triangles, ^ee F%-. .5.^- Tn the Triangle EAB, the Sides 
EA and AB are known from the Field Book, and their contained 
Angle is known from the Bearing of the Sides. The other 
Angles and the Side EB may be found by Oblique Trigonome- 
try, Case III. ; and then there will be the three Sides to find 
the Area. In the Triangle EBC, the Side BC is known from 
the Field Book, and the Side EB is found as above mentioned ; 
the Angle EBA is also found as above ; this subtracted from 
the Angle ABC, which may be found from the bearing of the 
Sides AB and BC, will leave the Angle EBC : there will then 
be the two Sides and their contained Angle to find the third 
Side ; and this being found, there will be the three Sides to find 
the jliea. In the Triangle EDC, the Sides DE and DC are 
known from the Field Book, and their contained Angle is 
known from the bearing of the Sides. The Side EC and the 
Area may be found as above. 

It is recommended to the Learner to make these calcuki- 



SURVEYING. 



49 



tioiis, as it wUl improve him in the knowledge of Trigonome- 
try. 

iN'ole. Two Sides and their contained Angle being given, the Area may- 
be found by Prob. IX. Rule 4. 



Another JWethod of protracting Fields. 

Without drawing parallel Lines at the end of each Side, a 
Field may be protracted by the Angles made by the several 
Sides ; and the Angle made between any two Sides may be 
found by the following Rules. 

Rule 1. If the course or bearing of one of the Sides is 
northerly and the other southerly, one easterly and the other 
westerly, subtract the less Course from the greater, the remain- 
der will be the Angle between them. 

Rule 2. If one is northerly and the other southerly, and 
both easterly or westerly, add both Courses together ; the sum 
will be the Angle between them. 

Rule 3, If both are northerly or southerly, and one easter- 
ly and the other westerly, subtract the sura of both from 180<^ ; 
the remainder will be the Angle between them. 

Rule 4. If both are northerly or southerly, and both east- 
erly or westerly, add 90°, the less Course, and the Comple- 
ment of the greater together ; the sum will be the Angle be- 
tween them. 

To protract a Field according to the preceding Rules is pre- 
ferable to the method of doing it by parallel Lines, though it 
may not be so easy to the Learner at first. It is difficult to 
draw parallel Lines with perfect accuracy, particularly without 
a parallel Rule ; and a small deviation from a true Line may 
make considerable difference in the Plot of a Field. 



Example II. 

FIELD BOOK. See Fig. 58. 

Ch. L, 
AB. N. 160 30^ E. 22. 
BC. N. 82 E. 19.60 
CD. S. 17 E. 24. 
DE. S. 37 W. 22. 
EA. N. 49 W. 25.20 



Area 85 Acres, 




M 



50 



SURVEYING. 



To draio « Plot of this Field, according io the preceding 

Rl'LES. 

Having drawn the Side AB, according to the directions be- 
fore given for laying off the first Course and Distance, com- 
pare the first and second Courses together, and they will be 
found to be both northerly and both easterly ; consequently, 
the Angle between them is found by Rule 4, as follows : 90° 
added to 16° 30'' the less Course, and 8° the Complement of 
the greater, the sum is 114° 30^, for the Angle at B. Compare 
the second and third Courses, and they will be found to be one 
northerly and one southerly, and both easterly ; consequently, 
according to Rule 2, 82° the second Course added to 17° the 
third Course, the sum 99° is the Angle at C. The third and 
fourth Courses are both southerly, and one easterly and the 
other westerly. The Angle between them at D is 126° ; for 
170 the third Course added to 37° the fourth Course is 64^^ 
which subtracted from 180© leaves 126°, according to Rule 3. 
The fourth and fifth Courses are one southerly and the other 
northerly, and both westerly. According to Rule 2, 37° the 
fourth Course added to 49° the fifth Course, the sum 86° is the 
Angle at E. 

A little practice will render this mode of protracting a Field, 
familiar and easy, and an attention to the Courses will show in, 
%vhat direction the Angle is to be made. 



Example III. 
FIELD BOOK. See Fig. 66. 








SURVEYING. 














Ch. L. 


AB. 


N. 


560 


15^ 


E. 


21.60 


BC. 


N. 


26 


30 


E. 


13.44 


CD. 


S. 


71 


30 


E. 


18.96 


DE. 


S. 


26 


30 


E. 


13.44 


EF. 


S. 


71 


30 


W. 


18.96 


FG. 


S. 


45 





E. 


8.47 


GH. 


S. 


63 


30 


E. 


13.44 


HI. 


N. 


45 





E. 


8.47 


IK. 


S. 


26 


30 


E. 


13.44 


KL. 


S.. 


45 





W. 


8.47 


LM. 


s. 


63 


30 


W. 


13.44 


MN. 


N. 


76 





W. 


24.73 


NA. 


N. 


36 


45 


W. 


30. 


Acres Rood 


Rods 








Area 167 — 


1 — 


-30 









5-1 



The above Field may be protracted, and its Area calculateii; 
according to the directions given in the preceding Examples. 



Several Field Books io exercise the Learner in 'plotting Fields and 
calculatino- their Area. 

















Ch.L. 




No. I. 


Rods. 


8. 


N. 


53015^ 


W. 


11.60 


1. 


N. 150 b^ E. 


320 


9. 


N. 


36 45 


E. 


19.20 


2. 


N. 37 30 E. 


160 


10. 


N. 


22 30 


E. 


14. 


3. 


East 


120 


11. 


S. 


76 45 


E. 


12. 


4. 


S. 11 E. 


200 


12. 


s. 


15 


W. 


10.85 


5. 


South 


216 


13. 


s. 


16 45 


W. 


10.12 


6. > 


West 


160 






Acres Roods Rods. 


7. 


S. 36 30 W. 


160 




^reallO — 


2 — 


23 


8. 


N. 38 15 W. 


136 














Acres Roods ' 


Rods 






No. III. 


Rods. 




Area 744 — 3 — 


28 


1. 


S. 


65040^ 


W. 


49.7 








2. 


s. 


67 15 


W. 


34.5 




No. 11. 


Ch.L. 


3. 


s. 


54 


w. 


17.9 


1. 


N. 750 0^ E. 


13.70 


4. 


s. 


20 


w. 


5.S 


2. 


N. 20 30 E. 


10.30 


5. 


s. 


7 30 


E. 


29.4 


3. 


East 


16.20 


6. 


N. 


83 


E. 


107.4 


4. 


S. 33 30 W. 


35.30 


7. 


N. 


5 50 


W. 


22. 


5. 


S. 76 W. 


16. 


8. 


N. 


18 30 


w. 


46. 


6. 


North 


9. 






Acres Rood Rods, 


7. 


S. 84 W. 


11.60 




Area 34 — 1 — 


19 



42 








SURVEYING. 












No. IV 




Rods. 










Rods. 


1, 


N. 


430 0' 


W. 


12.44 


16. 


.N. 


18030^ W. 


39. 


2. 


N. 


64 


W. 


8. 


17. 


N. 


86 


5 E. 


26.7 


3. 


N. 


52 


w. 


14.60 






Acres Rood Rods 


4. 


N. 


37 5 


w. 


61.36 




Area 48 • 


— 1 — 12 


5. 
6. 


N. 
N. 


15 30 
20 40 


w. 
w. 


21.76 
44.60 
















No 


.VII. 


Ch. L. 


'7. 


N. 


88 20 


E. 


167.60 


1. 


N. 


0045^ W. 


9. 


8. 


S. 


34 40 


E. 


71.20 


2. 


N. 


19 


30 W. 


5.36 


9. 


S. 


75 


W. 


69.72 


3. 


N. 


23 


W. 


4.09 


10. 


s. 


55 


W. 


64.60 


4. 


N. 


41 


35 W. 


6.15 


11. 


s. 


25 


W. 


18.12 


5. 


N. 


3 


W. 


36.75 




Acres Roods Rods. 


6. 


S. 


86 


50 W. 


13.33 




,B.rea 


97 — 2 


— 29 


7. 


N. 


a 15 W. 


17.65 I 












8. 


N. 


85 


45 E. 


12.56 1 






No.V 




Rods. 


9. 


S. 


2 


10 E. 


8. 1 


1. 


S. 


11030^ 


W. 


34.6 


10. 


N. 


86 


45 E. 


7.38 ' 


2. 


s. 


63 20 


E. 


93.6 


11. 


S. 


3 


15 E. 


13.20 


3. 


N. 


4 


W. 


34.9 


12. 


N. 


87 


E. 


29.92 


4. 


S. 


89 65 


E. 


40.1 


13. 


N. 


49 


20 E. 


^ 4.04 


5. 


N. 


5 20 


W. 


35.5 


14. 


North 




2.23 


6. 


N. 


69 40 


W. 


60. 


15. 


N. 


60 


35 E. 


6.50 


7. 


S. 


78 


W. 


30.6 


16. 


S. 


22 


50 E. 


17.94 


8. 


N. 


67 20 


w. 


1.2 


17. 


s. 


34 


W. 


3.50 


9. 


S. 


72 30 


w. 


10.4 


18. 


s. 


41 


W. 


3. 


10. 


s. 


66 55 


w. 


15.2 


19. 


s. 


22 


60 W. 


9.25 




Acres Rood Rods, 


20. 


s. 


3 


40 E. 


2.64 




Jlrca 


41 — 1 


— 34 


21. 


s. 


86 


W. 


2,50 












22. 


s. 





25 W. 


14.50 






No. VI 


, 


Rods. 


23. 


s. 


2 


w. 


5.38 


1. 


S. 


340 0^ 


E. 


42.8 


24. 


s. 


10 


E. 


11.75 i 


2. 


S. 


29 


E. 


69.4 


25. 


s. 


86 


W. 


34.60 I 


3. 


S. 


64 50 


W. 


63. 






Acres Roods Rods 1 


4. 


S. 


25 


E. 


4. 




£r.ea 268 


— 3 — 


^ 1 


5. 
6. 


S. 
N. 


66 30 
25 


W. 

W. 


39. 

4. 










1 






- No 


VIII. 


Rods " 


7. 


S. 


64 45 


w. 


32.2 


1. 


S. 


603O'' E. 


19.1 


8. 


N. 


30 30 


w. 


18.3 


2. 


S. 


63 30 E. 


14.36 


9. 


N. 


56 30 


E. 


34.5 


3. 


S. 


67 


E. 


10.68 


10. 


N. 


64 


E. 


12.5 


4. 


N. 


88 


E. 


13.3 


11. 


N. 


49 


E. 


14. 


5. 


S. 


31 30 W. 


32.44 


12. 


N. 


26 10 


w. 


19.3 


6. 


S. 


31 55 W. 


96.5 


13. 


N. 


21 


w. 


18.3 


7. 


s. 


33 25 W. 


34.9 


14. 


N. 


44 10 


w. 


18. 


8. 


s. 


20 45 E. 


3.68 


15. 


N. 


64 40 


E. 


30.5 


9. 


s. 


16 15 W. 


64. 











SURVEYING. 




53 


10. 


N. 


52O30' 


W. 


12.8 


21. 


N. 360 0^ 


E. 


41.56 


11. 


s. 


45 


W. 


18.24 


22. 


S. 68 


E. 


80.6 


12. 


s. 


69 


W. 


21.4 


23. 


N. 44 30 


E. 


20.4 


13. 


s. 


12 40 


W. 


9.4 


24. 


N. 2 30 


W. 


41. 


14. 


s. 


84 20 


W. 


9.5 


25. 


N. 14 45 


W. 


62.32 


15. 


N. 


22 15 


W. 


24. 


26. 


N. 16 


W. 


14.8 


16. 


North 




9.8 


27. 


N. 1 45 


W. 


14.8 


17. 


N. 


29 15 


W 


30.6 


28. 


N. 82 30 


w. 


99. 


18. 


N. 


44 26 


W 


21.8 










19. 


N. 


61 30 


W 


23.1 




Acres Rood Rods 




20. 


N. 


41 


W 


10.8 


Area 135 — 1 - 


- 15 





CASE V. 

To survey a field from one station, at any place within the Field, 
from which the several Angles may be seen. 

Take the Bearing of the Angles, and measure their Distance 
from the Station. 



FIELD BOOK. See Fig. 61. 



Fig. 61. 










Ch. L, 


Station to A. 


N. 


20OW. 


8.70 


B. 


N. 


60 E. 


10. 


C. 


N. 


87 E. 


11.40 


D. 


S. 


15 E. 


10.50 


E. 


S. 


60 W. 


12. 


F. 


N. 


65 W. 


8.78 



To p'otract this Field. 
Draw a Meridian Line as N. S. From some point in that 
Line as a Centre lay off the Bearing and Distance to the several 
Angles, and draw Lines from one Angle to another, as AB, BC. 
^'^ &c. 

N . 



CD, 



-54 



SURVEYING, 



To find the Area. 

The Area may be calculated according to Prob. XII. by 
measuring Diagonals and Perpendiculars ; or more accurately 
according to Prob. IX. Rule 4. 

As the Bearing and Distance of the Lines from the Station 
lo the several Angles are knowrf, two Sides and their contained 
Angle are given in each of the Triangles into which the Plot 
!3 divided ; the Area may, therefore, be readily calculated by 
the Bule above referred to. 

J\''ote. As in the operation, the Logarithm of Radius is to be subtracted 
from the Sum of the other Logarithms, it may be done by rejecting the 
Left-hand figure, without the trouble of putting down the Ciphers and 
subtracting. 



Triangle 


aAB. 




Triangle 


aDE. 




aA, 8.70 - 


- 


0.93952 


aD, 10.50 - 


. 


1.02119 


aB, 10 - 


. 


1.00000 


aE, 12 


. 


1.07918 


Sine AaB, 80° - 


. 


9.99335 
1.93287 


Sine DaE, 75° - 
Doub. Area, 122 


^ 


9.98494 


Doub. Area, 85.7 


2.08531 


Triangle 


aBC. 




Triangle 


aEF. 




aB, 10 


- 


1.00000 


aE, 12 


. 


1.07918 


aC, 11.40 - 


. 


1.05690 


aF, 8.78 


. 


0.94349 


Sine BaC, 27° 


aCD. 


9.65705 
1.71395 


Sine EaF, 55° 
Doub. Area, 86.3 

Triangle 


aFA. 


9.91336 


Doub. Area, 61.8 


1.93603 


Triangli 




aC, 11.40 - 


. 


1.05690 


aF,8.78 - 


. 


0.94349 


aD, 10.50 - 


. 


1.02119 


aA, 8.70 - 


. 


0.93952 


Sine CaD, 78° - 


aAB 


9.99040 
2.06849 


Sine FaA, 45° - 
Doub. Area, 54 - 

85.7 


- 


9.84948 


Doub. Area, 117 


1.73249 


Triangle 








aBC 


- 


51.8 








aCD 


. 


117. 








aDE 


- 


122. 








aEF 


.. 


86.3 








aFA 

Vrea 
Vrea 


- 


54. 




... ,., 


Double J 


516.8 




s 


25)84 





SURVEYING. 



55 



84 
4 



Acres Roods Rods 
.irea 25 — 3 — 14.4 



3)36 
40 

14)40 



CASE VI. 

To survey a Field from some one of the .Angles, from which th^ 
others may be seen. 

From the stationary Angle take the Bearing and Distance to 
each of the other Angles, with a Compass and Chain. 

Fig. 59. 



FIELD BOOK. Sec Fig. 59. 












Ch. L. 


FG. 


N. 


70O 


W. 


14.60 


FA. 


N. 


50 


W. 


18.20 


FB. 


N. 


30 


W. 


16.80 


FC. 


N. 


10 


w. 


21.20 


FD. 


N. 


7 


E. 


16.95 


i^E. 


N. 


30 


E. 


8.50 



To di'aw a Plot of this Field. 

Draw a Meridian Line to pass through the stationary Angle 
as at F. From the Point F, lay off the Bearing and Distance 
to the several Angles, and connect them by Lines, as FG, FA, 
FB, &c. 

The Area maybe calculated as taught in the preceding Case. 



66 



SURVEYING. 



CASE vn. 

To survey a Field from two Stations within the Field, provided 
the several Angles can be seen from each Station. 

Find the Bearing from each Station to the respective Angles ; 
and also the Bearing and Distance from one Station to the 
other. 

Fig. 62. 



FIELD BOOK. See Fig. 62, 






First Station. 




AC. 


N. 380 


30^ 


E. 


AD. 


S. 69 





E. 


AE. 


S. 69 





W. 


AF. 


N. 63 





W. 


AG 


N. 21 





w. 


AH. 


North. 







Second Station. 

BC. S. 820 0^ E. 

BD. S. 17 E. 

BE. S. 2S W. 

BF. S. 49 W. 

BG. N. 76 W. 
BH. N. 24 W. 

Stationary Line AB. N. 14° E. 20 Chains. 

To protract this Field. 

At the first Station A, draw a Meridian Line and lay off the 
Bearings to the respective Angles ; draw the Stationary Line 
AB, according to the Bearing and Distance ; at B, draw a Me- 
ridian Line parallel to the other, and lay of the Bearings to 
the Angles, as taken from this Station ; from each Station draw 
Lines through the Degree which shows the Bearing of each 
Angle, as marked by the Protractor or Line of Chords, and the 
Points where those Lines intersect each other will be the An- 
gles of the Field. Connect those angular Points together by 
Lines, and those Lines will represent the several Sides of the 
Field. 



SURVEYING. 



Oi 



CASE VIII. 

To Sui'vey an inaccessible Field. 

Fix upon two Stations, at a convenient distance from the 
Field, from each of which the several Angles may be seen ; 
from each Station take the Bearing of the Angles ; and take 
the Bearing and Distance from one Station to the other. 

Fig. 67. 



FIELD BOOK. See Fig-. 67. 












Ah^ 




"H^3 










S5 


- 


s- 


Fh 


'st Station. 








Second Station. 




AE. 


N. 90 


15'' 


E., 


BE. 


N. 50O 0^ 


W 


AF. 


N. 16 





E. 


BF. 


N. 29 15 


w 


AG. 


N. 14 


30 


E. 


BD. 


N. 24 


w 


AD. 


N. 39 





E. 


BG. 


N. 21 30 


w 


AH. 


N. 40 





E. 


BH. 


N. 5 


E. 


AC. 


N. 72 





E. 


BC. 


N. 20 30 
Ch. L. 


E. 



Stationary Distance AB, S. 88© 30^ E. 19.20. 

The directions given in the last Case for plotting the Field, 
will apply in this Case also ; and the Area in this and the pre- 
ceding Case may be calculated in the manner pointed out in 
Case IV. by dividing the Plot into Triangles and measuring 
Diagonals and Perpendiculars. Or the Sides may be found by 
Trigonometry, and the Area calculated Arithmetically, as 
already taught. 



5& 



SURVEYING. 



CASE IX. 



To stiTvey a Field where the boundary Lines are very irregular^ 
vjithout noticing loith the Compass every small Bend. 



Fig, 68. 



Begin near one corner of the 
Field, as at A, Fig. 68. and 
measure to the next large Cor- 
ner, as B, in a straight Line ; 
noticing also the Bearing of 
this Line, From the Line 
take Offsets to the several 
Bends, at Right Angles from 
the Line ; noticing in the 
Field Book at what part ofM 
the Line they are taken, as at 
A 1, H 2, 1 3, B 4. Proceed 
in the same manner round the 
Field. In the Figure the dot- 
ted Lines represent the sta- 
tionary Lines, and the black 
Lines the Boundaries of the Field 




FIELD BOOK. 



Bearing and Distance, 


Offsets 


Bearing and Distance. 


Ofiisets 




Ch. L. 


Ch. L. 


Ch. L. 


Ch. L. 


AB. N, 85° 0' E. 


11.20 


0.56 


EF. S. 57° 50' W. 8.20 


0,40 




at 6.40 


1.40 


at 1. 4 


0.36 




8.26 


0.36 


2.96 


0.33 




the end 


0.36 


5.88 
the end 


1. 
12 


BC. N. 70 20' E. 


7.96 
at 2.36 






0.36 FG. S. 27° 40' E. 7.06 


1.20 




4.28 


0.96 at 2. 


0.24 




the end 


0.30 the end 


0.16 


CD. N. 62° 0' W. 


4.68 




GA. 3. 250 20' W. 6.48 






at 4.34 


0.30 


at 3.80 


0.80 








the end 


U.40 


DE, N. 110 10' w 


. 4.20 


0.30 





SURVEYING. 5^ 



To protract this Field. 

Draw the stationary Lines according to the directions in 
Case IT. From A make an Offset of 56 Links to I ; measure 
from A to H 540 Links and make the Offset H 2, 140 Links | 
measure from A to I 826 Links and make the Offset I 3, 36 
Links ; at B make the Ofiset B 4, 36 Links. Proceed in the 
same manner round the Field, and connect the ends of the Off- 
sets by Lines, which will represent the Boundaries of the 
Field. 



To find the Area. 

Find the Area within the Stationary Lines as before taught ; 
then of the several small Trapezoids, Parallelograms and Trian- 
gles made by the stationary Lines, Offsets and boundary Lines, 
and add the whole together : thus, add 66 Links the Offset A 
1 to 140 Links the Otiset H 2 and multiply their sum 196 by 
half 640 the length of the line AH, and the Product 52920 
Square Links will be the Area of the Trapezoid AH 21 : again^' 
add 140 the Offset H 2 to 36 the Offset I 3 and multiply their 
Sum 176 by half 286 the length of the Line HI, and the pro- 
duct 25168 Square Links will be the Area of the Trapezoid 
HI 32. Proceed in the same manner to calculate the Area of 
ajl the Trapezoids, Triangles, &c. 



CASE X. 

To survey a Field by taking Onsets both to the Right and Left , 
thai is, within and without the Field, as occasion shall require, in 
consequence of the Stationary Lines crossing the boundary Lines : 
also, by Intersections, that is, taking the bearing of an inaccessible 
Corner from two Stations. 

The directions given in the preceding Case, together with 
the following Field Book, will show the Learner how to sur- 
vey a Field like the following, and also to protract it when sur- 
veyed. 



60 



SURVEYING. 



Fig. 69. 



FIELD BOOK. ,See U 
Fis:. 69. 




Offsets 
to the 
Left. 


Bearing and Distance. 


Offsets 
to the 
Right. 

Ch. L. 


Remarks. 


Ch. L. 
1.12 

3.40 

1.25 


Ch. L. 

AB. N. 88" 0' W. 22.12 
at 4.25 
7.40 
13. 


A Tov/er bears from, 
A. N. 48° W., 


0.45 


BC, N. 27°45'W. 21.12 
at 4.10 
10.25 
15. 


1.20 
1.15 


From B the Tower 
bears N. 38° 30' E. 




C 1. S. 82° 15' E. 5.45 
1, 2. N. 70 E. 13.25 
2 D. N. 20 E. 3.36 




From C go into the 
Field to 1, on account of 
some impediment on or 
near the boundary Line. 
At D, you get into another 
Corner of the Field. 




DF. S. 35O0'E. 15.15 




E, an inaccessible Corner, 
bearsfromD. S. 65°30'E. 


2.20 
2.32 


FA. S. 150 15' E. 15,10 

at 1.20 

7.45 

12.25 


0.36 


E, the inaccessible Corner, 

bears from F 

N. 4" W. 



JVbfe. To draw a Tree, House, Tower, or any other remarkable object, 
in its proper place, in the Plot of a Field — From any two stations, while 
surveying the Field, take the bearing of the object , and the intersec- 
tion of the Lines, which represent the bearings, will determine the 
place of the object, in the same manner that the Tower is drawn in the 
Fi,a;ui-e. 



SURVEYING. 61 



Tofaid the Area of the above Field. 

Find the Area within the stationary Lines, and then of the 
several small Trapezoids, &c. remembering to distinguish 
those without the stationary Ijines from those which are within. 
Subtract the Area of those within the stationary Lines from 
the Area of those without, and add the Remainder to the Area 
contained within the stationary Lines ; the sum will be the 
whole Area of the Field. 



SECTION in. 

Rectangular Surveying, or an accurate method of calculating 
the Area of a Field Arithmetically, from the Field Book, vdihout 
the necessity of protracting it and measuring with a Scale and Di- 
viders, as is commonly practised. 

I. Survey the Field in the usual method with an accurate 
Compass and Chain, and from the Field Book set down, in a 
Traverse Table, the Course or Bearing of the several Sides, 
and their length in Chains and Links, or Rods and Decimal 
parts of a Rod ; as in the 2d and 3d Columns of the following 

EXAMPLK. 



6,'i 



SURVEYING. 







—■-*- 




-cCTaTOUic 




.™^- 




1 


1 


2; ' ' 




00 


M 


05 


Wl 


fa- 


W M 1 M 






5J 


CO 


^ 


CO 




^ ?! 1 ?! 






oa 






00 


s. - 




^ 







00 


<^ 


p- "^ 






■-< en 






(-« 











.0 


° 


c 






j^ 




W 




=> 








*. 


1;^ 


Ot 


j> 


w 1 


*» 


» 


a- 




t(^ 





© 


W:- 


» 


I 







D- c 


>-> t- 






















^s K) 












J5 W 




. ^ 


Ul w 


03 C5 


^ 




, 






-J 1-^ 


->J M 


►u <I 


^ 


• 








> 


5> <t 


I-" to 


• 


05 O 


W 




• 






• t 


S5 W 


a; »< 








03 1)5 




01 en 


*» A 










01 u^l ; 


to to 






>oco 


, 






CO 


hfe. tO! • 


io ^ 




Ha 


■" 


• 













1 W 




•-» tn 






Jl 00 


• 
















1 




OS 00 


t« to 


« ts 




rf^ tp' 




: 




• 1 P P 





Ji.*. 


© 


w 






• 


• 


1 CJ> 01 





J5 UO 


<« ■<« 


to 






• 


• • 


3) l(^ 


tl^O 


» c« 


*• •- 






to ts 


to to 


W rfi 


. 












>*>■ »f»-i r* t^ 


W 05 




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• 






^ 


"■» Qo' 


<! ^ 


«» - 


• 










t^ tCw 


to tn 








J3 




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to 


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-T 


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*- 


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M 


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to 


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In 


to 

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to 




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to 









30 
30 


to 

00 


00 

01 




















bO 


l»i 








en 












=> 


3> 






«1 


(?5 











• 








5 






tMj 




• 








— i 





gg^ 







00 










• 


0' 


XI 






w 












-4 






_o> 









1 




1 


35 


© 


























fp 




to 






-i 
















I-* 




<33 


X 












Ml 




to 




P 


» 


' 








T. 









■vt 


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• 






^S- 









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«= 


-.-•^•raosc 





^-™«. 


• , .. .. 









19143.9019 Sum of South Areas 
4245.4016 North Do, 



2)14898.5003 Douhle Area of the Field 

Acres 744)92501 
4 

Roods 3)70004 
40 

Rods 28)00160 



Acres Roods Rods 
744 — 3 _ 28 



SURVEYING. 63 

2. Calculate by Right Angled Trigonomktrt, Case 1, or 
find by the Table of Difference of Latitude and Departure,* 
or by the Table of Natural Sines,| the northing or southing, 
easting or westing, made on each Course, and set them down 
against their several Courses, in their proper Columns, marked 
N. S. E. W. 

Js^ote. To determine whether the Latitude and Departure for any parti- 
cular Course and Distance are accurately calculated, square each of 
them ; and if they are right, the Sum of their Squares will equal the 
Square of the distance, for the following reason : the Latitude and De- 
parture represent the two Legs of a Right Angled Triangle, and the 
Distance the Hypothenuse ; and it is a Mathematical truth, that the 
Square of the Hypothenuse of any Right Angled Triangle is equal to 
the Sum of the Squares of the two Legs. 

3. If the Survey has been accurately taken, the sum of the 
nortbmgs will equal the southings, and the eastings will equal 
the westings. If, upon adding up the respective Columns, these 
are foimd to differ very considerably, the Field should be again 
surveyed ; as some error must have been committed, either in 
taking the Courses or measuring the Sides. If the difference 
is small, a judicious, experienced Surveyor will judge from the 
nature of the ground or shape of the Field surveyed, where 
the mistake was most probably made, and will correct accord- 
ingly. Or, the northings and southings and the eastings and 
westings may be equalled by balancing them, as follows ; sub- 
tract one half the difference from that Column which is the 
largest, and add the other half to that Column which is the 
smallest ; and let the difference, to be added or subtracted, be 
divided among the several Courses, according to their length. 

In Example I. the upper numbers are the northings, &c. as 
found by a Table of Difference of Latitude and Departure, 
The several Columns being added, the northings are found to 
exceed the southings 47 Links, and the westings to exceed the 
eastings 24 Links. They may be balanced by taking 24 Links 
from the northings, and adding 23 Links to the southings ; and 
taking 12 Links from the westings, and adding 12 Links to the 
eastings. Take from the first Course of the northings 12 Links, 
from the second 7, and from the third 5 ; to the first southing 
add 7 Links, to the second 10, and to the third 6 : add to the 
first easting 3 Links, to the second 3, to the third 4, and to the 

* For an explanation of this Table, and the manner of using it, see tb^ 
remarks preceding the Table. 
t Bee the Remarks preceding the Table o-f Natural Sings. 



^4 SURVEYING. 

iburth 2 ; take from the first westing 5 Links, from the secoud 
4, and from the third 3. The lower numbers will then repre- 
sent the northings, &c. as balanced. 

4. These Columns being balanced, proceed to form a De- 
parture Column, or a Column of Meridian Distances ; which 
shows how far the end of each Side of the Field is east or west 
of the station where the calculation begins. This Column is 
formed by a continual addition of the eastings and subtraction 
of the westings ; or by adding the westings and subtracting the 
eastings : See Example I. 

The first easting 20.74 is set for the first number in the De- 
parture Column ; to this add 24.38 the second easting, and it 
makes 45.12, for the second number; to this add 30.04 the 
third easting, and it makes 75.16, for the third number; to this 
add 9.56 the fourth easting, and it makes 84.72, for the fourth 
number ; the fifth Course being south, it is evident the Meri- 
dian Distance will remain the same, therefore, place against it 
the same easting as for the preceding Course; from this sub- 
tract 39.95, the first westing, and it leaves 44.77, for the sixth 
Course ; from this subtract 23.75, the second westing, and it 
leaves 21.02, for the seventh Course ; from this subtract 21.02 
the last westing, and it leaves 0.0; to be set against the last 
Course, which shows that the additions and subtractions have 
been accurately made. For as the eastings and westings equal 
each other, it is evident that one being added and the other 
subtracted, there will in the end be no remainder. 

5. The next step in the process is to form a second Depar- 
ture Column, the numbers in which show the Sum of the Me- 
ridian Distances at the end of the first and second, second and 
third, third and fourth Courses, &c. 

The first number in this column will be the first in the other 
Departure Column ; to which add the second number in that 
Column for the second in this : for the third add the second and 
third ; and for the fourth, the third and fourth ; and so on till 
the Column be completed. See Example I. 

The first number to be placed in the second Departure Co- 
lunm is 20.74 ; to this add 45.12, and it makes 66,86, for the 
second nimaber; to 45.12 add 75.16, and it makes 120.28,. for 
the third number; to 75.16 add 84.72, and it makes 159.88 for 
the fourth number ; to 84.72 add 84.72, and it makes 169.44 
for the fifth number; to 84.72 add 44.77, and it makes 129.49 
for the sixth number ; to 44.77 add 21.02, and it makes 65.79 
for the seventh number; to 21.02 add 0.0, and it makes 21.02 
for the eighth number. 



SURVEYING. 



65 



6. When the work is thus far prepared, multiply the several 
numbers in the second Departure column by the northings or 
southings standing against them respectively ; place the pro- 
ducts of those multiplied by the northings in the column of 
north areas, and of those multiplied by the southings in the co- 
lumn of south areas ; add up these two columns and subtract 
the less from the greater ; the remainder will be double the 
area of the field in square rods or square chains and links, 
whichever measure was used in the survey. 



Fig. 63. 



Demonstration of the preceding Rules. 
See Fig. 63. and Example 1. 




51. ...VH 

The dotted line A 2 represents the northing, and the line 2 B 
the easting made by the first course ; these multiplied together^ 
that is, 77.15X20.74=1600.0910, which is double the area of 
the triangle A2B, as is evident from the Rule to find the area of 
a triangle, Prob. IX. Rule 1. This number is to be placed for 
the first number in the column of north areas. The line 3C 
represents the sum of the eastings made by the first and second 
courses, which is 45.12 the second number in the first departure 
column ; if to this you add 20.74 the length of the line 2B you 
have 65.86, which is the second number in the second depar- 
ture column, and which represents the sum of the two lines 3C 
and 26. These two lines with the line 2, 3 which represents 
the northing made by the second course, and the line BC, one 
of the sides of the field, form a Right Angled Trapezoid. Now^ 
by the rule to find the area of such a Trapezoid, See Prob. X. 
65.86X31.66=2085.1276, double the area of the Trapezoid 
2 BC 3. Place this product for the second number in the co- 
lumn of north areas. 



66 SURVEYING. 

To the line 3C add CD 30.04, the easting made by the third 
course, and you have 75.16. which is the sum of the eastings 
made by the three first courses, and the third number in the 
first departure column. To this add 9.66, the easting of the 
fourth course, and you have 84.72, the length of the line IE, 
which represents the sum of the eastings made by the four first 
courses, and is the fourth number in the first departure column. 
These two, viz. the lines 3D 75.16 and IE 84.72, added to- 
gether make 159.88, the fourth number in the second departure 
column; which, being multiplied by 49.15, tke length of the 
line 3, 1 which represents the southing made by the fourth 
course, will give double the area of the Trapezoid 1 ED 3. 
The number thus produced is 7858.1 020^ which is to be placed 
for the first number in the column of south areas.. 

The fifth course being due south, it is evident the sum of the 
eastings will remain the same as at the end of the fourth 
course ; that is, the line 4F equals the line IE, which is 84.72. 
These added make 169.44, the fifth number in the second de- 
parture column. This, being multiplied by 54.10, the length 
of the line EF, which is the southing of the fifth course as cor- 
rected in balancing, and the same as the line 1, 4 — will give 
double the area of the parallelogram 1 EF 4, which is 
9166.7040, the second number in the column of south areas. 

From the line AF 84.72 subtract 39.95, which is a west 
course, and it leaves 4G 44.77, the sum of the eastings, or the 
Meridian distance, at the end of the sixth course, and the sixth 
number in the first departure column. From this subtract 23.75 
the westing made by the seventh course, and you have 21.02, 
the length of the line 511, which is the Meridian distance at the 
end of the seventh course, and the seventh number in the first 
departure column. The line 4G 44.77 added to the line SH. 
21.02 make 65.79, the seventh number in the second departure 
column. This being multiplied by 32.21, the length of the 
line 4, 5 — which is the southing of the seventh course, will 
give double the area of the Trapezoid 4GH5, which is 2119- 
.0959, the third number in the column of south areas. 

The line H5, 21.02, is the westing of the last course, and 
the last number in the second departure column. This being 
multiplied by 26.65, the length of the line 5A, and the northing 
of the last course, produces 560.1830, which is double the area 
of the Triangle A5H, and the last number in the column of 
north areas. 

J^ote. It will be observed that against the third and sixth Courses there 
are no Areas ; the reason is, that these Courses being one e?i5t and tU« 



SURVEYING. 67 

other west, there is no northing or southing to be multiplied into them : 
regard can therefore be had to them only in forming the Departure Co- 
lumns. 

By inspecting the Figure, and attending to the preceding 
illustrations, it will be seen that the three North Areas repre- 
sent double the Area of the Triangle A2B, the Trapezoid 2BC3, 
and the Triangle A5H, all of which are without the boundary 
lines of the field : also, that the three South Areas represent 
double the Area of the Trapezoid 3DE1, the Parallelogram 
1EF4, and the Trapezoid 4GH5 ; and that these include not only 
the field but also what was included in the North Areas. There- 
fore the North Areas subtracted from the South, the remainder 
will be double the Area of the field, coatained within the black 
Jines. 



Additional Diredimvs and Explanations. 

The northings and southings may be added and subtracted 
instead of the eastings and westings ; then there will be two 
Latitude columns instead of Departure columns, and the num- 
bers in the second Latitude column must be multiplied into 
the eastings and westings, and you will have east and west 
Areas. 

When the coiirse is directly north or south, the distance must 
be set in the north or south column ; when east or west, in the 
east or west column. There will therefore sometimes be no 
number to be added to or subtracted from the number last set 
in the Latitude or Departure column ; then the number last 
placed in the column must be brought down and set against such 
Course ; as in Example L at the 5th Course. It may also 
sometimes be the case that there will be no number to multiply 
into the number in the second Latitude or Departure column ; 
then that number must be omitted, and against such Course 
there will be no Area as in Example I. at the 3d and 6th 
Courses. 

When the northings or southings, eastings or westings, be- 
ginning at the top, will not admit of a continual addition of the 
one and subtraction of the other, without running out before you 
get through the several Courses, you may begin at such a Course 
as will admit of a continual addition and subtraction ; and when 
you get to the bottom go to the top, and you will end in cipher 



as 



SURVEYING. 



at th€ Course next above that where you began; as inExAMPLt 
il. which begins at the 9th Course to add the eastings and sub- 
tract the westings. 



Example II. 



Courses. 



iDist. 

iRods 



N. S. 



W. 



lN.75O0'E. 
2N. 2030E. 

3 East 

4 S. 33 SOW. 
58.76 OW. 
e.North 

6S. 84 OW. 
N. 6S15W. 
N. 3645 E. 
N.2230 E. 
S. 76 45 E. 
S. 16 OW. 
S. 16 45W. 



54.814.21 
4I.238.6i 

64.8 

141.2..... 

64 i 

36 36 ] 

46.4 

46.4 27.8 
76.8 61.5 
56 i51.7 

48 ! 

43.4 

40.5 



Idep. 
Col. 



!52.9i. • . 144.1 
14. 
64. 



2dep. 
Col. 



North 
Areas \ 



49 



.46 

.',21. 

'46, 

9 . . 



235.3 3341.26 
158.5 302.611680.36 

223.3 381.8 

77.9 145.4 368.7' 

62.1; 83.3 228.7 
.'■ 83.3;166.6 
i, 37.2 120.S 



37.2 0.0 
. . .! 46 
. . .: 67.4 
. . .114.1181.5 
11.2 102,9 217 
11.7 91.2191.1 



37.2 
46 
113.4 




Area 110 Acres, 2 Roods, 23 Rods, 



J^ote. In the above Example you might begin at the 4th Course to add the 
westings and subtract the eastinais ; or at the 6th Course to add the 
northings and subtract the southings : or at the 11th Course to add the 
southings and subtract the northings. So in every survey, some place 
may be found where you may begin to add and subtract, without run- 
ning out befor^ you get through all the Courses. 

When a field is very irregularly shaped, it will often happen 
that parts of the same Area will be contained in several differ- 
ent products in the columns of Areas ; but in the final result, 
one column being subtracted fi'om the other will leave what is 
Included within the boundary lines of the field. 



SURVEYING. 



69 



FfV. 64. 



Demonstratictn. 
See Fig. 64, and Ex- 
ample II. 




The Area standing against the 9th Coiu-se, which is where 
the calculation begins, is the Triangle I2K, all without the 
Field. 

The Area against the 10th Course is the Trapezoid 2KL35 
also without the Field. 

The Area against the 11th Course is the Trapezoid 4ML3. 
This is a South Area, and contains a part of the Field and also 
part of the preceding North Area. 

The Area against the 12th Course is the Trapezoid 5NM45 
part within and part Without the Field. 

The Area against the 13th Course is the Trapezoid 6AN5., 
part within and part without the Field. 

The Area against the 1st Course is the Trapezoid 6AB7, 
part within and part without the Field. This is a North Area, 
and to be ultimately subtracted from the South Areas ; but this 
includes a part of the preceding South Area, viz. tlte space 
nAso; it will, however, be seen hereafter that this same space 
is included in another South Area, This North Area contains 
also a part of the first North Area, viz. the space 6no7 ; but 
the same space is also included in another South Area. 

The Area against the 2d Course is also a North Area, and is , 
the Tx'apezoid 7BCS. This Trapezoid contains the space 
sBCx, without the Field ; the space osxw, within the Field ; 
and the space 7ow8, without the Field. But the space osxw 
will be contained in the next south Area ; and the space 7ow8, 
which was contained in the two first North Areas, will be con- 
tained in the next South Area. 

By examining the whole Figure in this manner, it will be 
^een that the North Areas contain all without the Field that is 

R 



70 SURVEYING. 

taken into the Calculation, and some of it twice over ; they 
also contain part of the Area within the Field. The South 
Areas contain all within the Field, and all without the Field 
that is contained in the North Areas. They also contain, 
twice over, so much of the Field as is included in any of the 
North Areas ; and likewise, twice over, that part without the 
Field which is contained twice in the North Areas. So that sub- 
tracting the North from the South Areas leaves double the Area 
of the Field. 

This method of calculating the Area of a Field by the 
Northings, Southings,Eastings, and Westings, divides the Field, 
with a certain quantity of the adjoining ground, into Right An- 
gled Trrangles, Right Angled Trapezoids, Parallelograms, or 
Squares, as may be seen by the Figures. It may therefore 
with propriety be called Rectangular Surveying. 



A Useful Problem. 

To find the true Area of a Field xvhieli has been measured by a 
Chain too long or too short. 

Calculate the Area as if the Chain was of a true length,, then 
institute the following Proportion : 

As the Square of the length of the true Chain ; 

Is to the Area, as found by the Chain made use of; 

So is the Square of the length of that Chain ; 

To the true Area of the Field. 

Example. 

Suppose a Field, measured by a Two Rod Chain 3 Inches 
too long, is found to contain 41 Acres 1 Rood and 33 Rods, 
what is the true Area t 

As the Square of 33 Feet, the true length of a Two Rod 
Chain ; Is to 41 Acres 1 Rood and 33 Rods ; So is the Square 
of 33 Feet 3 inches, the length of the Chain used in the Sur- 
vey; To 42 Acres and 13 Rods. 33 Feet=396 Inches. 
396 X 396=156816 Square Inches. 

41 Acres 1 Rood 33 Rods=6633 Rods. 

33 Feet 3 Inches=399 Inches. 399 X 399=159201 square 

-» y\ f> fl p C 

139201 X 6633—156316=6733 Rods. 
6733-~l 60=42 Acres 13 Rods, the true Ai'ea. 



SURVEYING. ^ 71 

PART II. 

Laying out Land. 

PROBIjEM I. To lay out any number of Acres in the form 
of a Square. « 

Annex 5 Ciphers to the number of Acres, which will turn 
them into Square Links, the Square Root of which will be the 
Side of the Square in Links. 

Example. It is required to lay out 810 Acres in the form of a 
Square. 

Jlnswer. Each Side of the Square must be 9000 Links, or 
90 Chains. 

PROBLEM IL To lay out any number of Acres in the form 
of a Parallelogram, whereof one Side is given. 

Divide the number of Acres, when turned into Square Links, 
by the given Side ; the Quotient will be the Side required. 

Example. What must be the lomxest side of a Parallelogram, 
which is to contain 25 Acres, when the shortest side is 5 
Chains and 50 Links 1 

Jinswer. 2500000-r-650=4545 Links for the longest Side. 

PROBLEM III. To lay out any number of Acres in a Field^ 
3, 4, 5, 6, SfC. times as long as it is broad. 

Divide the Acres, when turned into Square Links, by the 
proportion between the length and breadth ; the Square Root 
of the Quotient will be the shortest Side. 

Example. It is required to lay out 100 Acres 5 times as long 
as it is broad. 

Answer. 10000000-^-5=2000000 the Square Root of which 
is 1414 Links for the shortest Side, and the longest will be 7070 
Links. 

PROBLEM IV. To make a Triangle which shall contain a 
given number of Acres, being confined to a certain Base. 

Double the given number of Acres, to which, annex 5 Ci- 
phers, and divide by the Base ; the Quotient will be the Per- 
pendicular in Links. 

Example. Upon a Base of 40 Chains to lay out 100 Acres in 
a Triangular form. 

Answer. 5000 Links or 50 Chains will be the length of the 
Perpendicular. 



72 



SURVEYING. 



The Perpendicular may' be erected 
from any part of the Base : Thus, the 
Triangle ABC. See Fig. 55. is the 
same as ABE, each containing 100 
Acres. 



When the given Base is so situa- 
ted that a Perpendicular of suffi- 
cient length cannot be erected there- 
from, continue the Base as from B to 
D. Fig. 56. from which erect the 
Perpendicular DC, and complete 
the Triangle ABC, which will con- 
tain 100 Acres. ^, 




Fig. 56. 




^.......fD 



PART III. 

Dividing Land. 

As different Fields are so variously, land many of them irre-r 
gularly shaped, and as they are required to be divided in many 
different proportions, it is difficult to give Rules which will ap* 
ply to particular cases. The business of dividing Land must 
therefore be left, in a great measure, to the skill and judgment 
of the Surveyor ; who, if he is well acquainted with Trigono- 
metry, and with measuring Land, will not find it difficult, after 
a little practice, to divide a Field in such a manner as shall be 
desired. If he has before him a plot of the Field, and knows 
the number of parts into which it is to be divided, and the pro- 
portion which each part. is to bear to the others, he will readily 
find out where the dividing Lines are to be drawn. 

A few Rules and Examples will be given for the general 
instruction of the Learner. 

PROBLEM I. To cut off any numhe^- of Aa-es from a Square, 
■&r Parallelogram. 



SURVEYING. 



73 



Saj-^, as the whole number of Acres in the Field ; Is to the 
length of the Square or length or breadth of the Parallelo- 
gram ; So is the number of Acres proposed to be cut off; To 
their proportion of the length or breadth. 

PROBLEM II. To cut off any number of Acres by a Line 
proceeding from any Jingle of a Triangle. 

Measure the Base, or Side opposite the Angle from which 
the dividing Line is to be drawn ; Then say, As the number 
of Acres in the whole Triangle ; Is to the whole Base; So is 
the given numb'^r of Acres ; To their part of the Base. 

Fig. 67. 



Example. -See Fig. 67, 



In the Triangle ABC, which contains 48 Acres, it is required 
to cut off 18 Acres, by a Line proceeding from C to the Base 
AB, which is 40 Chains. 

As 48 : 40 : : 18 : 15 

Lay 45 Chains on the Base from B to D, and draw the Line 
CD. The Triangle will then be divided as was proposed ; 
BCD containing 18 Acres. 

PROBLEM III. To take off any given number of Acres from 
a multangular Field. 

Fis. 65. 





ExABIPLE I. -See Fig. 65. 



Let ABCD, &c. be the Plot of a Field containing 11 Acres, 
from which it is required to cut off 5 Acres. 

Join two opposite Corners of the Field as D and G, with the 

R2 



74 



SURVEYING. 



tiine DG (which you may judge to be near the partition Line) 
and find the Area of the part DEFG, which, suppose, may 
want 140 Rods of the quantity proposed to be cut off. Mea- 
sure the Line DG, which, suppose to be 70 Rods ; divide 140 
by 35 the half of^DG, and the Quotient 4 will be the length of 
a Perpendicular whose Base is 70 and the Area 140. Lay off 
4 Rods from G to I, and draw the Line DI, which will be the 
dividing Line. 



Example II, See Fis. 60. 



Let ABCD, &c. be a tract of land 
to be divided into two equal parts, by 
a line from I to the opposite side CD ;A 
to iind arithmetically on what part of 
the line CD the dividing line IN will 
fall ; or to find the Distance CN. 




FIELD BOOK. 



AB. N. 
BG. S. 
CD. S. 
DE. S. 
EF, S. 



19° 0' 
77 
27 
52 
15 30 



E. 
E. 
E. 

W. 
E. 



Rods. 

lOS 

91 

115 

58 
7G 



GF. West 

GH. N. 36° 0' W. 

HI. North 

lA. N. 62 15 W. 

Acres Rood Rods 
Whole Area 152—1 — 25 



Rod? 

70.9 

47 

64.» 

59 



Find the Area of the part lABCI, according to Section IIL 
Page 57, as follows : set the Latitude and Departure of the three 
first Sides, lA, AB, and BC, in their proper colwnns, in a Tra- 
verse Table ; and place as much southing, viz. 109.1, equal to 
the line CK, and as much westing, viz. 71.7, equal to the line 
KI, as will balance the columns. This southing and westing 
will be the Latitude and Departure made by the line CI. The 
Area of lABCI will be found to be 8722 Rods, which is less 



SURVEYING. ■" 75 

tiian half the Area of the whole Field by 3470 Rods, the quan- 
tity to be contained in the Triangle ICN. 

Find the bearinji and distance of CI by Right Angled Trigo- 
nometry, Case IV. as follows ; 

As CK, the southing of CT, 109 - . . _ . 2.03743 

: Radius 10.00000 

: : Kl, the westing of CI, 71.7 ------ 1.85552 

11.85552 
' 2.03743 

: Tangent Course S. 33° 20' W. 9.8180D 

As Sine Course 33° 20 - - - - - - - 9.73997 

: Departure KI 71.7 - - 1.85552 

:: Radius - - - - 10.00000 

11.85552 
9.73997 

: Distance IC 130 ------- - 2.11555 



J\fote. In this way the Course and Distance may be found from one Angle 
of a Field to another. 

Having found the line CI, divide 3470, the number of Rods 
to be contained in the Triangle ICN, by one half the line CI. 
viz. 65, the quotient will be the length of the Perpendicular 
PN, viz. 53.4. 

Now, by the bearings of CI and CD, it appears that they 
form an Angle of 60° 20^ ; wherefore, in the Triangle CPN 
are given the side PN 53.4, and the Angle at C 60° 20^ to find 
the Hjpothenuse CN. 



\s Sine. PCN 60O 20^ 
Side PN 53.4 
: Radius 



Hyp. CN 61.5 



9.93898 

1.72754 

10.00000 

11.72754 
9.93898 

1.78856 



Thus the dividing line must go from I to a point on the line 
CD, which is 61.5 Rods from C, The bearing and distance of 



78 SURVEYING. 

this line may be found by the directions given above for finding 
the bearing and distance of the line CI. Or, they may be found 
by Oblique Trigonometry, Case III. 



Another Method oj finding the Distance CJV*. 

Having ascertained the Latitude and Departure of the line 
CI, set them down in a Traverse Table ; find the Latitude and 
Departure of the line CD, and place them m the Table ; the 
diiference-between the northing of the line IC, and the southing 
of the Line CD will be the southing of the line DI, viz. 6.6 ; 
and the sum of the eastings of those lines, as they are both 
easterly, will be the westing of the line DI, viz. 123.9. Pro- 
ceed to calculate the Area of the Triangle ICD, which will be 
found to be 6622 Rods, nearest. 

J^ote. As in this Triangle two sides and their contained Angle are given, 
the Area^nay be found by Prob. IX. Rule 4, Page 38. 

Having found the Area of this Triangle, proceed to find 
CN according to Prob. II. Page 73, as follows: 

As the Area of the Triangle ; Is to CD the Base ; So is the 
quantity to be contained in the Triangle ICN; To.CNits pro- 
portian of the Base. 

As 6522: 115: : 3470 : 61.2 



A third method of finding the Distance CJV*. 

To the Logarithm of double the Area to be contained within 
the Triangle ICN add Radius; from this Sum subtract the 
Logarithmic Sine of the angle at C ; and from the Remamder sub- 
tract the Logarithm of the Side IC ; the last Remainder will be 
the Logarithm of the Side CN. 

The double Area of the Triangle ICN is 6940 ; the Angle at 
C is 60O 20^; the Side IC is 130. 

Double Area 6940 - - 3.84136 

Radius - - - - 10.00000 



13.84136 
Sine ICN 60O 20' - - 9.9389S 

3.90238 



SURVEYING. 77 

3.90238 
Side TC 130 - . - 2.11394 



Side CN 61.5 - - - 1.78844 



.Yole. Radius may be added by placing a Unit before the Index of tte 
Logarithm for the double Area, without the trouble of setting down 
the Ciphers. 



By JVatural Sines. 

Divide the Double Area by the Natural Sine of the givejo 
Angle, and that quotient by the given Side ; the last Quotient 
will be the Side CN. 

Nat. Sine of the Angle at C 60° 20^ 0.86892 

6940-~0. 86892=7986.92 

7986.92-~l30=61.43 



From the above the following general Rule may be drawn. 

To find the Side of a Trian0e when the Area is given, with 
one of the Sides and the Jingle contained between the given Side 
ajid the Side required. 

To the Logarithm of double the Area add Radius; from 
this Sum subtract the Logarithmic Sine of the given Angle, 
and from the Remainder subtract the Logarithm of the given 
Side; the last Remainder will be the Logarithm of the Side 
required. 

Or, By JVatural Sines: Divide the double Area by the Nat. 
Sine ol the given Angle, and that Quotient by the given Side ; 
the last Quotient will be the Side required. 



CONCLUDING REMARKS. 

Other methods of surveying Fields are taught by some 
authord on this subject. The preceding, however, will be 
found most useful in actual practice. Other instruments be- 
sides those mentioned in this Book are also sometimes used| 
such as the Plain Table, Semicircle, Perambulator, Theodov 



78 SURVEYING. 

lite, &c. But of these instruments very little use is made in 
New-England ; and they are not often to be met with. For 
general practice none will be found more useful than a common 
Chain, and a Compass upon Rittenhouse's construction. A 
Surveyor should also provide himself with an Offset Staff, ten 
Links in length, and accurately divided into Links. This 
should be made of firm hard wood, and will be found very con- 
venient in taking Offsets, and also in measuring the Chain ; 
which should be often done, as from a variety of causes a Chain 
is liable to become inaccurate. 

It will be observed that in this Work there are no descrip- 
tions of Mathematical and Surveying instruments. The Com- 
piler omitted such descriptions from a belief that nothing which 
can be written on the subject will enable a person to under- 
stand them without an actual inspection of the instruments 
themselves, and some instruction from those acquainted with 
them. 

The general principles here taught may be applied to the 
surveying of Townships, Roads, Rivers, Harbours, &c. 



APPENDIX. 



CSF THE VARIATION OF THE COMPASS AND ATTRACTION OP THE 
NEEDLE. 

The Variation of the Compass is the number of Degrees that 
the Magnetic Needle points from the true North, either East 
or West. This differs in different places, and in the same 
place at different times. It is, at present, in Connecticut, a 
few degrees to the Westward. That is, the Needle points to 
the Westward of North, and is gradually approaching the true 
North. 

The following method of ascertaining the Variation, by the 
North Star, has been adopted by many Surveyors, as the 
most eligible to be practised on Land. It was communicated 
to the Compiler by Moses Warren, Jun. Esq. of Lyme, an 
experienced Surveyor, with permission to publish it. 

The Star commonly called the North Star, is not directly 
North but revolves round the Pole in a small circle, once in 24 
hours. It cannot therefore be due North but twice in that 
period ; and that is within a very few minutes of the time 
when a Star, called Alioth, in the Constellation of Ursa Major, 
or the Great Bear, is directly over or under it. There is also 
another StEir nearly in an opposite direction from the Pole, 
called Gamma, in the Constellation of Cassiopeia. When 
these three Stars Text vertical the North Star is very near the 
Meridian ; and whc-a they are horizontal, it is at its greatest 
Elongation, that is, at its greatest distance East or West 6f the 
Pole, and on the same side as the Star in Cassiopeia. The 
Variation may be calculated when the Star is on the Meridian, 
or when at its greatest Elongation ; more accurately, however, 
at the latter period, because its motion being then neajjy verti- 



80 



APPENDIX. 



cal for some time gives the observer a better opportunity to 
complete his observation.* 

To find the Elongation of this Star in any Latitude, its Declina- 
tion must be known; that is, its distance North of the Equator. 
This being found, institute the foUovring Proportion : 

As Co-Sine of the Latitude ; Is to Radius ; So is Co-Sine of 
the Declination ; to Sine of the Elongation. 

The Declination of the North Star, January 1, 1810, was 
8SO 17^ 28^^, and increasing at the rate of about 19 seconds and 
One half annually. 

The following Table Shows the Elongation, in several 
different Latitudes, for 5 years successively. It is calculated 
for the first of January in each year ; and in using it, if the time, 
when the Elongation is required, be past • the middle of the 
year, take it for the beginning of the next year. 

A Table showing the Elongation of the JVorth Star. 



Latitude. 


1820 


1821 


1822 


1823 


1824 


380 


20 5^ 34^^ 


20 5/7// 


20 4^39^'' 


20 4/ 13^^ 


20 3/47'^ 


39 


2 


7 23 


2 


6 54 


2 


6 25 


2 5 59 


2 


5 33 


40 


2 


9 12 


2 


8 41 


2 


8 14 


2 7 46 


2 


7 20 


41 


2 


11 11 


2 


10 40 


2 


10 12 


2 9 44 


2 


9 18 


42 


2 


13 10 


2 


12 39 


2 


12 11 


2 11 43 


2 


11 16 


43 


2 


15 22 


2 


14 51 


2 


14 22 


2 13 54 


2 


13 26 


44 


2 


17 33 


2 


17 4 


2 


16 34 


2 16 5 


2 


15 37 



* The following Figure exhibits a view of the relative situation of these 
Stars as they appear, when in a horizontal position : or when the North 
Star is in its greatest Eastern Elongation. 

The Great Bear. Cassiopeia- 



* Aliotb 



Pole( 



North StSr 



Ganima ^ 



APPENDIX. Si 

"The Elongation for the Latitude of the observation being- 
calculated, or taken from the above Table, proceed to find its 
range, according to the following directions ; 

Take a pole 18 or 20 feet in length; to the end of it fasten a 
small line ; raise it to an elevation of 45° or 50° ; and support 
it by two crotches of suitable height to keep it firm in its 
place. At the end of the line, near the ground, fasten a weight 
of half a pound cr more, which should swim in water to prevent 
the air from moving the line. Southward of the line, fix a 
Compass sight, or other piece of metal or wood, with a narrow, 
perpendicular aperture at a convenient height from the ground, 
say about 2 or 2 1-2 feet ; and let it be so fixed that it can be 
moved a small distance East or West at pleasure. Let an as- 
sistant hold a light either NE or NW.of the line, nearly as 
high as the range from the sight to the North Star, in such a 
position that the line may be plainly seen ; then, (the three 
Stars above mentioned being parallel or nearly so with the 
Horizon) move the sight-vane East or West, until through the 
aperture, the line is seen to cut the Star ; and continue to ob- 
serve, at short intervals, till the Star is seen at its greatest 
Elongation. Let a lighted candle be placed in an exact range 
with the sight-vane and line at the distance of 20 Rods or more, 
which should stand perpendicularly, be made fast, extinguished, 
and left till morning. Then the sight-vane, the line, and the 
candle, will be the range of Elongation, which observe accu- 
rately with a Compass ; and if the Elongation be East and the 
Tariation West, the former must be subtracted from the latter ; 
and if they are both West they must be added, anil their differ- 
ence or sum will be the true Variation. 



OF THE ATTRACTION OF THE NEEDLE. 

It is well known that any iron substance has an influence upon 
the magnetic Needle, attracting it one way or the other from 
the point where it would settle, were there no such attraction. 
A surveyor should therefore be careful to see that no iron is 
near the compass when taking a bearing. But as the Earth ic 
certain spots contains, near its surface, iron or other minerals 
which attract the Needle, it will frequently happen that it will 
point wrong. To ascertam whether this is the case, the sur- 
veyor, at each station, should take a back view of the one last 
left ; and if he finds that the compass does not reverse truly, he 

S 



62 APPENDIX. 

may be sure, provided the compass be accurately graduated and 
placed horizontally, that he either made a mistake at the last 
station, or that in one or the other of the stations, the Needle 
was attracted from the true point. When he finds a place 
where he suspects there is an attraction, he should go a few 
rods backward or forward, and see whether the Needle points 
differently. In this way he may prevent mistakes in his field 
notes, by putting down a wrong course. To take back sights 
is particularly necessary in running long lines, and laying out 
new lands, where the Needle is the only thing to guide the sur- 
veyor. 

By practice and experience a knowledge will be acquired on 
this subject, and with regard to many other things in surveying, 
which cannot be taught by books ; and after all the directions 
which can be written, the practitioner will frequently find oc- 
casion for the exercise of his own judgment. 

A Rule to find the difference between the 'present variation of the 
Compass, and that at a time when a Tract was formerly sur- 
veyed, in order to trace or run out the original lines. 

Go to any part of the premises where any two adjacent cor- 
ners are known ; and if one can be seen from the other, take 
their bearing ; which, compared with that of the same line in 
the former survey, shows the difference, But if one corner 
cannot be seen from the other, run the line according to the 
given bearing, and observe the nearest distance between the line 
so run and the corner ; then work by the following proportion : 

As the length of the whole line, 

Is to 57.3 degrees,* 

So is the said distance, 

To the difference of variation required. 

Example. 

Suppose it be required to run a line, which, some years ago, 
bore N, 45° E., distance 20 chains, and in running this line by 
the given bearing, the corner is found 20 links to the left hand ; 
what is the present bearing of this line ? 

* 57.3 degrees is the Radius of a circle (nearly) in such parts as the cir- 
cumference contains 360. 



APPENDIX. 83 



Ch. Deg. 
As 20 : 57.3 : : 
100 20 

2000 1146.0 
60 



2000)68760(34 Minutes. 
Answer — 34 Minutes to the left hand is the allowance re- 
quired, and the line in question bears N. 44© 26^ E. 



The compiler of this work acknowledges himself under ob- 
ligations to George Gillett, Esq. Surveyor General of the state 
of Connecticut, for the following illustrations, remarks, and 
miscellaneous questions, considering them Ciilculated to be use- 
ful to the learner, and the practical surveyor. They came to 
hand too late to be inserted in their proper places, in the body 
of the work, and are here put together in the Appendix. 



Remarks on the Irregularities of the Magnetic Needle. 

By a statute of this state, applicants for the appointment of 
County Surveyor are required to be well skilled in point of 
science in the theory of the most approved methods of survey- 
ing lands. It is also as necessary that they should be as well 
skilled in practical surveying. A practical knowledge must be 
acquired by experience, and no one can have a thorough know- 
ledge of correct practice without being made acquainted with 
the imperfections and irregularities of the Magnetic Needle. 

It is supposed, by most people, that this instrument, in all 
places, points directly to the Poles of the earth, and that it re- 
mains as permanent as the Poles themselves — an infallible 
guide.* This is a mistaken idea. A fevv remarks on this sub- 

* There is one line around the globe on which there is no variation. The 
general course of this line, on this side of the globe, is from northwest to 
southeast, but is crooked and irregular iii its course. According to Dr. 
Holly's chart, made in 1700, the line of no variation crossed the meridian 
of London in 55® South latitude — crcssed the equator in 17° W. longi- 
tude — ^fiom thence, by various windings, to the island of Bermuda, fro;u 



84 APPENDIX. 

ject will here be offered, and some facts respecting it will be 
stated. 

Notwithstanding the great utility derived from the Magnetic 

thence nearly a west course until it struck the continent near Charles- 
ton, in South Carolina. This line is not stationary, but is ever varying 
its position ; and, notwithstanding the irregularity of its courses, it 
never crosses itself. About 1756, another variation chart was made, when 
it was found that the line had fallen so far to the ^vest that it struck the con- 
tinent near the coast of Florida. On the east side of this line, the Magnetic 
Needle points to the west of north, and on the west side it points to the 
east of north, and a regular increase of either east or west variation is found 
from it, depending on the course that is taken. The line of no variation 
now runs through Pennsylvania, and not far from Norfolk, in Virginia. 
When the Connecticut Western Reserve was surveyed into townships, the 
variation at that place was easterly from one to two degrees. In 1813, at 
New-Orleans, the variation was easterly, about eight or nine degrees. In 
1701, at Philadelphia, the variation was westerly, eight degrees and a half. 
In 1794, at the same city, the west variation had diminished to one degree and 
a half, which proves that the progress of the line of no variation had been 
from west to east. In 1813, by observations at this city, it was found that 
the west variation had increased to about two or three degrees. By a series 
of observations, commenced at Hebron in Connecticut, by the writer of this, 
in 1805, and continued to 1813, it was found that the west variation during 
that period increased more than half a degree. The result of these obser- 
vations agree with those at Philadelphia, that there had been a retrograde 
motion of the Needle. Since 1313, the west variation has diminished, or 
certainly it has not increased. The west variation at Hebron is now (1825) 
a few minutes more than five degrees. In 1580, at London, the Magnetic 
Needle pointed eleven degrees and a half to the east of north, which proves 
that the line of no variation was east of that place. The east variation 
diminished until 1657, when the line of no variation arrived there and soon 
passed by ; of course west variation began, and continued to increase until 
1806, when it exceeded twenty-four degrees. 

The line of no variation must have had a rapid progress through the At- 
lantic and through a great part of the United States, to have arrived at 
Charleston in 1700, and at the coast of Florida in 1756. The present bear- 
ing of all old lines in this state prove that there has been a considerable de- 
crease of west variation since the first surveys were made ; which also proves 
that the progress of the line of no variation, in the United States, has, for 
a long time, been from west to east. How far the line of no variation pro- 
gressed westward in the interior of this country before it turned, no one can 
tell. It is unaccountable how the west variation in London should increase, 
while at Philadelphia it was diminishing, when both places are on the same 
side of the line of no variation. The variation of the Needle has long been 
a subject of much perplexity. Observations have been made in abundance. 
Many facts have been ascertained, but the diflSculty is, they are not reducible 
to system. The polarity of the Magnetic Needle, with its variations anel 
irregularities, is a hidden mystery, which is never to be searched out by man. 
It is sufficient in itself, without any other evidence, to cause the reflecting 
Jiiind to wonder at, admire, and adore the wisdom, knowledge, and power 
of HIM who planned and directs it. 



APPENDIX. 85- 

Keedle, it cannot be relied on where great accuracy is requiredp 
on account of the irregularities to which it is subject, such as 
its annual motion in variation, its diurnal motion, and, what is 
attended with greater difficulty, its local attraction. When an 
©Id course is given to renew a line, it cannot be depended on, 
en account of the difference in variation between the time of 
the first running and the renewal of it. 

No annual rate can be fixed on for the variation of the Mag- 
netic Needle, as its motion is much more rapid in some years 
than in others. By observations made at London during a pe- 
riod of more than two hundred years, it appears that in some 
years the motion of the Needle was rapid, in others, but little 
would be discovered, and, in some years, the motion was retro- 
grade. There is no regularity in its motion in any place. 

Another difficulty in retracing a line from an old course or 
from one recently given is, that it is often found that two com- 
passes do not make the same course. It was well known to the 
celebrated Rittenhouse, that his compasses did not all agree, or 
make the same course, and he never was satisfied as to the rea- 
son of it. It has also been ascertained that different Needles 
do not point alike at the same place. French writers, on Mag- 
netism, have latel}' treated on this subject. Two compasses 
may differ a quarter of a degree or more or less, when no de- 
fect can be discovered in either- A survey may be taken as 
correctly with one as with the other. The question then natu- 
rally arises, which of the two is right ? The answer is, both 
are right ; neither of them points directly to the Poles of the 
earth, except on the line of no variation. All that can be said 
of them is, that one has a greater variation than the other, and 
that which has the least cannot have the preference^. The di- 
urnal motion of the Magnetic Needle is another defect in it. 
As the sun rises in the forenoon, and the earth becomes heated, 
it has an effect on the unknown something which gives polarity 
to the Needle, and turns the north end of it to the west. la. 
the afternoon and night following, it returns to its position,. 

For several years, the writer of (bis made observations with 
Rittenhouse's compass, to ascertain the diurnal motion ; and in 
the summer season usually found about a sixth part of a degree.. 
In the winter, but little or none could be discovered. The di- 
urnal motion of the Needle has been known in Europe about a 
century.* The local attraction is an irregularity to which the 
Magnetic Needle is subject. These are found oftener in hilly, 

' The diurnal motion is mentioned in Dr. Williams' History of Verniont, 

S3 



ae APPENDIX. 

broken lands, filled with ledges, than in level, feasible land, 
where there are no ledges. As attractions are out of sight, they 
i^iust be searched out, as before directed in this work, by locaL 
experiment. They often amount to a quarter, a half, and some-i 
times to a whole degree or more. The writer of this has kno wn^ 
a difference of more than five degrees within a distance of fortyl 
rods. 

When an old line is to be renewed where the bounds are lost, 
the circumstances attending the case must govern. These may 
be various, such as giving the lots on each side of the line and 
contiguous thereto, their full width or quantity, or by dividing 
the overplus or the wantage, as the case may happen. It would 
be difficult to mention all the circumstances which may govern, 
or which may serve as evidence in such cases. 

After all, the Magnetic Needle is the best guide that has ycl 
been discovered, and it cannot be dispensed with in land survey- 
ing ; but the surveyor who is best acquainted with it, will make 
as little use of it as he can. In small surveys, where one angle 
may be seen from another, the quantity of each angle may be 
taken by an instrument constructed for that purpose, vvithout 
the use of the Magnetic Needle ; and the sides may be measured, 
and one side, no matter which, may be made a meridian, and 
from that meridian courses may be calculated for the other sides, 
and the survey may be calculated by the rules of rectangular 
survejing. This method has been recommended by theorists, 
and the ingenuity displayed in the invention, together with the 
correctness of it, so far as it is practicable, must be acknow-- 
ledged ; but in larger surveys, it cannot be introduced to prac- 
tice, on account of the obstructions which intervene between 
the angular point and the termination of two contiguous lines 
which contain the angle : in such cases, the danger in taking the 
quantity of an angle will be greater than that of the Magnetic 
Needle. 

If in every town in the state, a meridian line was established by 
the motion of the heavenly bodies, and such meridians were 
X>erpetuated by durable monuments, whenever a survey was to 
be taken in the vicinity of a meridian, a surveyor might set his 
compass on it and note the variation found, and that variation 
should be inserted in the deed or in whatever writing or instru- 
ment by which the land is conveyed and made a record; this 
would assist a surveyor at an}"^ future period in retracing those 
lines, by setting his compass on the same meridian and allowiHg 
the same variation that was allowed when the survey was made. 
This would tend greatly to the security of landed property, and 



APPENDIX, 



^7 



perhaps would be the best remedy for the variation of the Mag. 
uetic Needle, and for the difference between two compasses 
which differ, that can be invented. 



On Practical Surveying. 

It would be no easy matter to describe all the different mev 
thods which may be taken in different cases, in taking the field- 
work of a survey. Only one case will be given here, which is 
represented by the following figure. See Fig, 1. 

Fig. 1. 

The survey was begun J th 2, 

at the corner numbered 
1. The corner numbered 
2 was in a pond. The 

course and distance were / xjT^. 

taken from 1 to jn, then 
from u\ to 11. The angle 
at 2 was a right one, of 
course there was a right 
angled triangle, wherein ^ 
the angles and hypothe- ^ 
iiuse were given, to find 
the sides ml and In. 
From n to 3, the course t2^^^ 

and distance were taken "'~-^. .''' 

on the line. The next '^ ** 

line ran through a thicket in a swamp, where nothing could bt 
done correctly. Courses and distances were taken from 3 to s,. 
thence to a-, thence to 4, and the course and distance of the line 
3 — 4 were calculated by a traverse from those courses and dis- 
tances. At the angle 5, a tree stood on a high bluff of ledges, 
inaccessible on either line terminating at that point. The 
course from 4 to 5 was taken at 4. Next, the course and dis- 
tance were taken from 4 to a, and from a the course was taken 
tO' 5. Next, the course and distance were taken from a to 6, 
and from 6 the course was taken to 5. Two oblique triangles, 
with the angles and one side in each, were given to find the sides 
4-^—5 and 5 — 6. The closing line ran through thick Ijushes and 
water, and the course and distance were taken on the dotted 




as APPENDIX. 

Une to the line 1 — 2, at a point twenty rods from 1 . The course 
and distance of 6 — 1 were calculated accoirdingly. 

Whenever a line runs through or over a place where it Is 
difficult to take either course or distance correctly,if, by taking 
u traverse around at a Utile distance, the surveyor can have 
level, clear land, and then calculates his course and distance by 
the traverse, he will be more likely to ascertain the true course 
and distance than by continuing on the line. 



Directions for running Lines. 

Many people suppose that a surveyor at the beginning of a 
Jine, by intuition or by some magic art, can set his compass di- 
rectly to the terminating point, whatever obstructions may in- , 
tervene, and that he needs no assistants ; but this is a mistaken 1 
idea. In running a line of considerable length, a surveyor 
should have two assistants to carry the chain, and two to carry 
flags, in whose ability and correctness he can confide, and a fifth ^ 
to use &n axe. If the surveyor is not furnished with such a set! 
of assistants, his employer need not place too much, confidence 
in his work. The flag staves should be as much as two and 
a half inches in diameter, or what would be better, two stripes _ 
of a board of that width and seven or eight feet in length. If* 
they are not so wide, they cannot be seen through the sights of 
t,he compass, at any great distance. On one end of each staff, 
a red flag of" a yard in length should be wound tight, and not left 
to hang loose and flutter in the wind. Red will be seen quicker 
through bushes than any other colour, and the brighter the co- 
lour the better. Being thus manned and equipped, at the be- 
ginning of the line, he must set his compass as near the true 
line as he can, or, what would be better, he may set up one of 
{he flags at the place of beginning, and go forward as far as he 
can have a fair view of the back flag, there set his compass on 
his random line, and send the other assistant as^far forward as 
he can conveniently see the flag. When each flag is clearly 
seen through the sights of the compass, the back flag must bo 
brought up and placed where the compass stood. In this naan-. 
ner, he must proceed on his random line, taking care each time 
he sets his compass to turn the sights to the back flag. Great 
care must be taken to keep these flags perpendicular ; also, the 
surveyor must keep the staff and the sights of his compass per- 
peadicuUir. A little leaning of the flags, or turning the sights 



APPENDIX. 88 

of the compass from a perpendicular, will make a crooked line. 
In looking through the sights of the compass to the flags, the 
surveyor must look as near the ground as he can, and, when 
practicable, the flag should be turned down, on account of the 
danger of being leaned when kept up. 

All obstructions, such as bushes, brush, &c. must be cleareil 
away. The random line must be measured, and at convenient 
distances, perhaps at every twenty rods, stakes must be set di- 
rectly in it. Every stake must be numbered, that no mistake 
may be mede in calculating, to set them in the true line. If, in 
the course of the random line, the Magnetic Needle does not 
traverse as at first, or traverse alike at different places, no re- 
gard must be paid to it — the two flags must direct the course ; 
neither should the surveyor be turned aside or terrified by the cry 
of either of the parties, You are wrong,You are wrong, (for he will 
most certainly hear it,) but he must continue his random line, 
until turning at right angles either to the right or to the left, aS 
the case may be, he will exactly strike the bound, or the point 
where a bound is to be erected ; there he may stop, and mea- 
sure the distance from the termination of it to the bound. Then, 
having the length of the random line and the distance to the 
true bound, he has the less of a right angled triangle, the hy- 
pothenuse will be the length of the true line ; also, the angle 
contained between the tree and the random line must be added 
to or subtracted from the course of the random line, (as the 
case'may happen,) which will give the course of the true line. 
Suppose the whole length of the random line is 2G0 rods, and 
the distance from the termination of it to the bound is 90 links, 
the calculation for setting the stakes on the true line may be 
made thus : — As the whole distance is to 90 links, so is 180, or 
any other 20 rods stake, t& the distance that such stake is to be 
moved. The answer is, the first stake is to be moved 9 links, 
the second 18 links, and so adding 9 links at each stake until the 
whole are moved at right angles from the random on the true 
line. Most of the crooked lines and consequent disputes and 
law-suits between farmers have arisen for the want of this care 
and attention. 

When a long line is to be run over a number of ridges and 
through intervening valleys, it should first be run and established 
from one ridge to another, and the intermediate spaces in the 
valleys may be taken afterward. By taking long sights there 
will be less danger of turning from a straight line. In all cases., 
the forward flag should be carried as far as it can be distinctly 
^en, unless it is at the termination of a line. 



98 APPENDIX, 



On keeping up Bounds. 



fl 



As the Magnetic Needle cannot be relied on in renewing lost 
boundaries, it is of the first importance that good, substantial 
bounds be made and kept up. In divisions or distributions of 
lands, erery surveyor ought to see that such bounds are erected. I; 
It is his business to see them made, and such bounds ought to be f 
described in deeds, or in the ins^truments by which the lands are 
Conveyed, and to be made a part of the record. By proper 
care and attention to this part of the business, almost an endless 
train of disputes may be prevented. Highways are attended j: 
with more difficulties of this kind than the location of any other! 
divisions of real estate. In laying highways, it is the custom ' 
to lay the centre lines, and order them to be of a certain width. 
In taking surveys of roads, stakes are usually set at the angles. 
When the roads are made, all these stakes are lost, and the tra- 
velling path is often built on one side of the centre ; but the 
bounds are lost, and after a tew years have elapsed, it is utterly 
impossible to tell where the road was laid. 

Surveyors who are employed on such business ought to de- 
scribe the angles, or as many as is practicable, in such a manner 
that the road may afterward be found. 

The follozieing Survey of a Road may serve as an Example. 

Beginning at a point on the centre of an old road, (here dcr 
scribe what road,) 14 rods westerly of the range of the west 
end of J. T.'s house, thence running S. 17° E. 84 rods 10 links 
to a point bearing West, 54 links from the S. W. corner of a 
large rock ; thepce, S. 5° E. 77i rods, to a point 77 links east 
of the centre of a large white-oak tree ; thence, S. 7° 30'' W. 
G7 rods 20 links, to a point bearing West 7 rods 10 links, from 
a perpendicular crevice in a rock. 

Enough of the survey is given to serve as an example. 

DIRECTIONS FOR USING THE COMPASS, AND CONCERNING ATTRAC- 
TIONS OF THE NEEDLE. 

In all cases the surveyor ought to set his compass at leasjt 
twice on each line, even if he has a fair view of the whole 
length of it. 

When there are local attractions, and no two places are 
found on the same line where the compass has the same tra- 



APPENDIX. 01 

\revse, the surveyor should take a medium and enter in his field 
book, noting such courses, as he may still have occasion to cor- 
rect them in his calculations. If in such cases he is at a loss 
what course to enter in his field hook, and suspects that some 
minutes may be added to, or subtracted from the course he 
enters in his book, let him prefix to such courses the sign of 
addition or subtraction as the case may be, which will often 
assist him in balancing his surveys. 

CONCERNING DRAWIJVG A MAP OF A FIELD. 

When a map is to be made of a multangular piece of land, 
whether a calculation or division is to be made from it, the sur- 
veyor should measure across the lot in some central place at 
least once, and in more places if convenient and the case may 
I'equire it. .By cross measures, the map will be made more 
correct. The surveyor should not be afraid of wearing his 
chain by measuring too much. When a survey is to be calcu- 
lated by plotting, it should not be laid on a scale less than ten 
rods to an inch. 

REMARKS ON BALANCING A SURVEY. 

In every survey which is accurate, the sum of the Northings 
will equal that of the Southings, and the Eastings will equal 
the Westings ; but this is not always an infallible proof that 
,the survey is accurate, for two errors may be committed, one 
exactly to balance the other, which no rule will detect ; but 
such cases do not often occur. In a survey of one hundred 
acres, whatever may be the number of the angles, the differ- 
ence between the two columns of Latitu.de and those of Depar- 
ture, ought not to exceed a rod for each, but to come within 
these limits if possible. 

If in such a survey either of the differences should exceed a 
rod, where the land is valuable and easily surveyed, it would 
be better to take a re-survey, or so far as to detect the error. 

Some authors have given rules for balancing surveys, which 
are indiscriminately applied to every line in the survey, which 
presupposes thvt a proportional error must have been commit- 
ted on each and all, both in courses and distances, when in al- 
most every survey, a part of the lines are on land so level and 
so clear from obstructions of any kind, that if the surveyor and 
c'hainmen attend to their business, they will not be likely to 



m APPENDIX. 

commit much error on them ; while other lines, on other parts 
of the same survey, are attended with so many difficulties, 
that when they have done their best, it will scarcely be possible 
for them to avoid some error, and the surveyor who takes the 
survey will best judge on what lines the errors were committed, 
and whether they are in the courses or in the distances. In all 
cases the corrections should be made on the lines containing 
the errors. When the errors are in the courses they should 
be corrected, and when the errors are in the distances, the cor- 
rection should be in them : or the corrections may be in both 
courses and distances as the surveyor may judge proper. 

When a course is northwesterly and southeasterly, or north- 
easterly and southwesterly, if the correction of it increases the 
latitude and diminishes the departure, or if it diminishes the 
latitude and increases the departure, so as to bring the differ- 
ences to an even balance, it is good evidence that the course 
contains some error. 

On Redangular Surveying. 

Rectangular Surveying is a name given to the method here 
treated of, by the late Governor Treadwell. 

A more appropriate name could not have been given ; for, 
the whole survey is reduced to right lined figures, such as 
triangles, trapezia, squares, and parallelograms. It is simply- 
multiplying the latitudes by the longitudes from a meridian 
from which the survey is calculated. 

The calculations are made from a meridian, drawn, either at 
the eastern or at the western extremity of the map. All the 
spaces lying between the field and the meridian from which the 
survey is calculated, and between the parallels of latitude of 
the northern and southern extremities of it, are included in the 
calculation. Parallels of latitude are drawn from each angle 
to the meridian, which are called meridian distances. 

In forming the column of meridian distances, when the meri- 
dian is drawn at the eastern extremity, the westings are added 
and the eastings are subtracted. When the meridian is drawn 
at the western extremity, the eastings are added, and the west- 
ings are subtracted. 

The meridian distances proceeding from each end of a Une, 
are added together, to form the column of double mean dis- 
tances, which the compiler of the foregoing work has called 
second departure column. 

The whole is illustrated by the following figure. See Fig. 2. 



APPENDIX. 



&3 



Directions for calculaiing meridian distances by several methods ; 
iils<i, for plotting a survey, from the several latitudes and meridian 
distances, ivithout the use of the protractor, or the line of chords. 



5W 



" 


u 






1 






« 




Ci 


■fri. 


1 M 


o 


l-I 




?» 


CO 


03 


!2| 


!2l 


:^ 


O 


1- 


en 

1 


O 

8 


8 


o 


8 


o 
o 




:^ 


H 


H 


^ 


o 


fe 


^ 


s 


§ 


fe 


SiO 


1 fe 


s 


8 


8 


o 

o 


8 


m'T 


CO 










g 


CO 
O) 


2! 


v9 
13 








CO 


en 


en 


00 


« 


g 


CO 

en 








J/3 


M\ B 


g 


lb 










§ 








en 


Cn 


o> 


H 


o 








CO 

en 


ta 


CO 

o 


n 3 


CO 


05 








:^ 


3 «l 
-1 CO 


fe 










8' 


o 


~1 

CS 


S 


h3 


OJ 


g 




g 


to 

CO 


OD 


-J 


;::; 


8 


O 














O 


S 




§ 


i 


CO 


•05 


g 




^ 


s^ 


s 


CD 


o 


CO 

o 


P 


ss 


11 


^ C3 


11 


feSg 


CO >- 

coa 




8^1 


05 ».. 
05 m 


05 00 


ES 


fis 


8§ 




cs 


J^ 


03 


en 


<r> 


CO 


a 




05 


o 
-J 


g 


8 


en 

o 


lb. 
en 


o 


OS 

2 






en 

00 
05 


s 


05 

••a 


> 


CO 




Cn 


00 


^ 


ta 


423 

11623 
3351 








CO 

> 


CO — to 

W 05 00 


CO 
09 


S 




_^ 




a 



T 



94 



APPENDIX. 



m 




Fig. 2. 
Meridian Dis- J^ 
tances, and Double 
Mean Distances, 
are more proper 
terms or names for 
the eighth and ninth 
columns, than first 
Departure, and se- 
cond Departure. 

The meaning of x 
the term Meridian 
Distance is the dis- 
tance made from 
any Meridian. It 
is not very essen- 
tial by what names 
the columns are 
called, as names 
have no effect on 
the final result. 

This survey is calculated from the meridian of the first sta- 
tion. 

To form the first column, marked at the top, Merid. Dist., 
set the easting 16.90 against the first station into the column, 
which is the meridian distance of 2, or the distance from 2 to 1 ; 
to this number add the next easting, and they make 22.11, 
the meridian distance of 3 ; to this number add the next east- 
ing, and they make 80.07, the meridian distance of 4 ; from 
this number, subtract the first westing, and 73.82 remains, the 
meridian distance of 5 ; from this number, subtract the next 
westing, and 70.33 remains, the meridian distance of 6, or the 
westing of the closing line. Subtract the last westing, and 
00.00 remains. This is on the principle of going around a 
circle. Next, form the column of double mean distances by 
adding two opposite sides of the different figures. Set the first 
Merid. Dist. into the column. To the first meridian distance, 
add the second, and they make 39.01, the double of the figure 
23ns. To the second, add the third, and they make 102.18, 
the double of the figure 34m». To the third, add the fourth, 
and they make 153.89, the double of the figure 45aw. To the 
fourth, add the fifth, and they make 144.15, the double of the 
figure 56as. To the fifth, add the sixth, and they make 70.33. 



APPENDIX. 9d 

The second column, marked at the top, Merid. Dist., is 
commonly called the Pennsylvania method. Only one column 
is used in finding the meridian distances, but the operation 
and final results are the same as that when two columns are 
used. This method is not so easily explained to the learner, 
but is preferable in practice only because an error may be com- 
mitted in forming the column of double mean distances which 
may not be discovered, but in this method an error cannot be 
committed without being detected. 

To form this column, set the first easting 16.90 in the upper 
place, and add it to itself and they make 33.80 ; to this number, 
add the next easting, and they make 39.01 ; add the same 
easting again, and they make 44.22 ; to this number, add the last 
easting, and they make 102.18 ; add the same easting again, and 
they make 160.14 ; from this number, subtract the first west- 
ing, and 153.89 remains ; subtract the same westing again, 
and 147.64 remains ; from this number, subtract the second 
westing, and 144.15 remains ; subtract the same westing again, 
and 140.66 remains ; from this number subtract the last westing, 
and 70.33 remains ; subtract the same westing again, and 00.00 
remains. 

The upper numbers in this column are the same as the double 
mean distances which stand against them. 

For the remainder of the process in finding the areas, pro- 
ceed as before taught in this work. 

The north area against the first station is the double of the 
triangle 12*; that against the second, is the double of the figure 
23ms ; that against the third, is the double of the figure 34«i» : 
the south area against the fourth station, is the double of the 
figure 45am ; that against the fifth, is the double of the figure 
56za ; that against the sixth, is the double of the triangle 6I0. 

The three north areas all lie without the field, and are bound- 
ed north on the line to4. The three south areas contain all 
within, and all without the field, which is included in the calcu- 
lation. It is obvious then that when the less is subtracted from 
the greater, the contents of the field will remain. 

Another column may be formed as the eleventh in this ex- 
ample, which, for distinction, is here called half departure. It 
contains half the sum of the numbers in the double mean 
column. These numbers when multiplied by their respective 
northings or southings, give the simple areas of the different 
figures. This method is preferable in practice, as the multi- 
plications are greatly diminished. When the last decimal in 
the double mean distance is an odd number, a unit may be taken 



m APPENDIX. 

off, and take half the remainder rather than annex another de - 
chnal. Perhaps this would not make the difference of a rod in 
a survey of one hundred acres, or the odd numbers in the last 
place of decimals may be balanced by sometimes adding a unit. 
If the numbers are diminished a trifle, it may be remarked; 
that, on account of the uneven surfaces, there is danger of 
making the distances too much rather than falling short of the 
true measure. 

To plot the foregoing Field from the several Latitudes and 
JVEeridian Distances, without the use of the protractor, or the line 
of Chords. 

First, set the northing of the first line from 1 to s ; set the 
northing of the second line from s to n ; set the northing of the 
third line from b to m ; set the southing of the fourth line from 
mto a; set the southing of the fifth line from a to z; next, 
from these points, draw parallels of latitude perpendicular to 
the meridian ; then, on these parallels of latitude, set the me- 
ridian distances of the several stations from sto 2, 16.90 ; from 
n to 3, 22.11 ; from m to 4, 80.07 ; from a to 5, T3.82 ; from z. 
to 6, 70.33. From one of these last points to another, draw 
the boundary lines of the field, and if the plan does not per- 
fectly close, it is because some error was committed in the 
process, or the scale ^as incorrect. In practical surveying, it is 
next to an impossibility in any case, to work so accurately that 
the survey will exactly close without some correction. The 
difference between the two columns of latitude, and the two 
columns of departure, are the legs of a right angled triangle, 
the hypothenuse of which will be the distance which the sur- 
vey will fail of closing. 

These differences, as before taught in this work, must be 
balanced, and the column of meridian distances must be formed 
by the numbers as balanced. When the survey is balanced, 
and this method of plotting is taken, the parallels of latitude 
must be laid down according to the balancing, and the map 
will perfectly close. 

When the courses and distances are corrected according to . 
the balancing, they will form a survey which will contain no 
ejror. 

N. B. Great care must be taken to keep the latitudes paral- 
lel and perpendicular to the meridian. The better to effect 
this, a meridian line may be laid on each side of a sheet^ or a 
kalf sheet of paper, as the occasion may require. 



APPENDIX. 



97 



The follmving Survey is calculated from a meridian running- 
through the map : of course, part of the meridia?!, distances are 
east, and part are tvest. See Fig. 3. 

Fig. 3. 




Ko. Courses 



1N60000'E 



Dist. 
Rods N. 



S. 



20.00 10.00 



2 S.30 OOE. 40.00! 



134.64 



3.8.70 00W.i70.00 23.94 



4n.30 OOW, 40.00 34.641 



^N.74 OOFJ5O.42 13.94! 



W. 



17.32 



17.32IE 
34.64E, 



20.00 



48.46 



65.78 



54.64E, 
74,64 E. 



8.86 E. 
56.92 W 



20.00 



76.92 W 
96.92W 



48.46,W 
00.00 



173.20 



1892.73' 



212. lOl 



2664.50 



675.53 



173.20 5444.86, 
173.20 



2)5271. 

A. Q. R. 

160)2635(16 1 35 
160 

1035 
960 



T3 



75 



98 APPENDIX. 

The column of meridian distances in this eiample is formed 
by adding twice, and subtracting twice against each station, as 
in the Pennsylvania method. Set the first easting in the upper 
place, which is the distance from a to 2, being east meridian 
distance ; add it to itself, and it makes 34.64 ; to this number, 
add the next easting, and they make 54.64, east meridian dis- 
tance from a to m ; add the same easting again, and they make 
74.64 ; from this number, subtract the first westing, and there 
remains 8.86 east meridian distance from i to s. As the first 
westing canndt be subtracted again, the last east meridian dis- 
tance, 8.86, must be subtracted from the first westing ; this 
crosses the meridian, and gives 58.92 west meridian distance 
in the lower place. Having crossed the meridian, the westings 
must now be added, and the eastings subtracted. 

To the 56.92 in the lower place, add the last westing, and 
they make 76.92 west meridian distance from r to u; add the 
same westing again, and they make 96.92 ; from this number, 
subtract the easting of the closing line, and there remains 
48.46 west meridian distance, from v to 1, or the easting of the 
closing line; subtract again, and 00 00 remains. Having com- 
pleted the column of meridian distances, next' multiply the 
upper number against each station, by its northing or southing, 
and set the products on the east side of the meridian, in their 
respective columns of north or south areas ; but on the west 
side of the meridian, the order is reversed ; the north products 
are setinfJhe column of south areas, and the south products are 
set in the column of north areas. The north area against the 
first station, is the figure 2z\a; the south area against the 
second station, is the figure mnia ; the south area against the 
third station, is the figure sxie ; the south area against the fourth 
station, is the figure mver, made by the northing of the fourth 
line ; the south area against the last station, is the figure v5rl. 

The foregoing columns of meridian distances might have 
been commenced, by setting the first easting in the lower place^ 
and the additions and subtractions, made as before directed, 
and the last subtraction would end in 00.00 at the upper place, 
against the first station. In this case, as there would be no 
upper number against the first station, there would be no 
product in either column of areas against it. The east meri- 
dian distance against the second station would extend no further 
east than the third station, and the meridian distance against 
the third station, would be on the west side of the meridian ; 
and the meridian distances, against the fourth and fifth stations, 
WQuld extend as much farther west, as the easting of the fiyst line., 



APPENDIX, 0^ 

The products against the second, fourth, and fifth stations.^ 
would be set in the column of south areas, and that against the 
third station, on account of its being on the west side of the 
meridian, would be placed in the column of north areas, and 
would be subtracted from the footing of the south areas. 

When a survey is calculated from a meridian running through 
the map, it is always best to set the first departure in the lower 
place, as it saves one multiplication^ 



On Distributing Estates. 

A farm is to bfe distributed among a number of heirs. A 
survey is made, and the difference between the columns of lati- 
tude, and between those of departure, are two rods for each. 
The survey is balanced, and calculated arithmetically, and is 
found to contain two hundred acres. The surveyor next draws 
his map, by which the divisions are to be made, according to 
the courses and distances. The plan does not close by nearly 
two rods and three-quarters. He next corrects the lines, and 
makes the map close as well as he can ; and when the divisions 
are made, they may not agree with the first calculation by two 
or three acres, or more. Should the map be drawn as before 
directed, by the meridian distances and the latitudes as balan- 
ced, it would close, and would be in exact conformity to the 
calculation made arithmetically. If the divisions are made 
arithmetically, without the use of the scale and dividers, the 
calculations must be made according to the balancing, or the 
divisions will not agree with the first calculation. 

It will be acknowledged by every experienced surveyor, that 
it is a difiicult matter to make the amount of a considerable 
number of divisions agree with the whole, when calculated by 
itself. 

It is the common practice in distributions, to make the di- 
visions with scale and dividers ; this method will answer very 
well provided the map is drawn on a large scale. 

The following is a useful rule in dividing lands, when any 
quantity is to be added to, or taken fi*om, a division in the form 
of a triangle. 

Having the area, the contained angle, and one side of a tri- 
angle given, to find the adjoining side, including the angle. 



100 APPENDIX. 



Rule. 



To the sine of the given angle, or its supplement if obtuse, 
add the logarithm of the given side ; subtract radius from this 
sum, and subtract the remainder from the logarithm of the 
double area, the last remainder will be the logarithm of the 
side required. 

In taking a survey, go around with the sun, not that you can 
work more correctly, or that it will have any effect in calcula- 
ting, but when you put your courses and distances on your map 
they will follow around with the lines, from the left to the 
right. 

Wherever you begin, set your compass on the angle and cause 
a stake or a flag-staff to be erected at the next. When your 
line runs over a hill, cause a stake to be erected at each end of 
it, and take your station on the top of the hill, directly between 
them. If bushes obstruct the sight, make an offset, or set your 
compass a little distance from the line, from whence you may 
see the back flag, and cause the forward flag or stake to be set 
against the bound in a direction with the compass and the back 
flag. When the line is measured, measure the distance from 
the flag to tiie bound, and calculate your true course by Trigo- 
nometr}'. If your next line is of such a distance that you can- 
not see through the whole length of it, run as near the true 
line as you can, and if you do not exactly strike the bound, 
measure the distance from the termination of your random line, 
and calculate your course as before directed, or if you can dis- 
cover a tree standing near the termination of your line, take 
the course and distance to that, thence to the bound, and calcu- 
late your true course and distance. 

By practice and experience, a method for taking courses will 
soon become familiar, in all cases. In measuring bills and in- 
clined surfaces, the horizontal distances must be taken. A 
plummet should be suspended from the end of the chain, when 
it is levelled. Where hills are very steep, the surveyor should 
assist the chainmen, and when the best is done in levelling and 
plumbing the chain, judgment must frequently be called mto 
exercise. Even when rises and descents are easy, there is 
dacjger of making too much measure. In such cases, chainmen 
often make allowances, but the surveyor would do better to 
keep them to close measure, and from the shape of the ground 
judge himself what allowances ought to be made. If he is ex- 
perienced in his business, he will form a more correct judgment 



APPENDIX. 101 

than inexperienced chainmen. Particular care must be taken 
that the chain is carried on a straight line, and that, it is well 
straightened. When a tally is ended, and the hinder chainman 
brings up the sticks, they must be counted. 

When on counting the sticks it is discovered that one is lost., 
the chainmen should not leave the chain and go back to find it. 
but, from the last mark, should measure back to the point where 
the tally began, to see whether one chain is lost from their mea- 
sure. Many blunders in this way have been left undetected by 
not taking this care. 

A careful accurate chainman never lost a stick or miscounted 
a tally. Young surveyors should practice much for their own 
instruction, and should make correct practice familiar, before 
they offer their services. It is as necessary that they should 
spend some time in acquiring a practical knowledge, as it is that 
they should spend any time in acquiring a knowledge of theory, 

A young surveyor should bear in mind that if he is detected 
in one error ia the beginning of his practice, it will be more to 
his disadvantage than to be detected in two when he shall be 
well established. If an error is committed in a survey, it is 
not against the surveyor provided he detects and corrects it, 
but if he cannot detect and correct his own errors, that is suffi- 
cient evidence of his deficiency in point of knowledge and 
skill. 



Form of a Field Book, 

Beginning at a murstone at the southwest corner, 
Rods Links 
40 00 to a white -oak tree., 
30 00 to a heap of stones, 
60 00 to a maple tree, 
36 00 to a pine tree, 
40 00 to a spruce tree, 
70 12 to the place of beginning. 
When a survey is calculated by chains and links, the numbers 
are less than when it is calculated by rods and decimal parts. 
Every method by which the numbers are diminished is an im 
provement. In a hilly country, the two-pole chain is prefera- 
ble and is more commonly used, because it can be levelled 
better. 

Hills are often found so steep that even th,e Iwo-pole cbgirv 
cannot be levelled,, 



1. 


N. 


250 


00'' E. 


2. 


N. 


10 


00 E. 


3. 


N. 


76 


00 E. 


4. 


S. 


10 


00 W. 


6. 


s. 


5 


00 W. 


6. 


s. 


85 


05 W. 



103 APPENDIX. 

MISCELLANEOUS. 

When a survey is calculated by chains and links, and the con- 
tents stand in acres and decimal parts of an acre, it may be mul- 
tiplied by the price of an acre, and the product will be the 
amount. 

Example. 

A piece of land, 12 chains and 25 links in length, and 10 
chains and 26 links in breadth, is sold for ^20 25, per acre ;— 
what is the price of it ? 

Length 12.25 
Breadth 10.25 



6125 
2450 

1225 

Acres and decimal parts 12.55G26 
Price of an acre 20.25 



6278125 
2511250 
2511250 

Answer ^254,26.40625 
The writer of these pages knows not who invented the fol- 
lowing rules for finding contained angles. For plainness, none 
of the kind exceeds them. 

N fi90 F 1 When the first letters are alike, and the two 
n' 4.4 w' • ^^^^ ^^^ unlike, add the degrees of both courses 

J together, which gives the contained angle. 
Q 790 F 1 When the two first and the two last letters are 
V a*! f' f" ^'^'^®' subtract one course from the other, and 

J the remainder will be the contained angle. 

}When the two first letters are unlike, and the 
two last alike, add both courses together, and sub- 
tract their sum from 180, the remainder will be 
the contained angle. 
'I When the two first and the two last letters are 
N. 570 W. i unlike, subtract one course from the other, the 
S. 25 E. I remainder from 180, and the remainder will be 
J the contained angle. 

Application of the above Rules. 
Two courses are given, viz. N. 67° W. and N. 28° E. to find 



APPENDIX. 103 

the angle. — Suppose yourself standing at the point where these 
courses meet. Reverse the letters oi" the first course, and they 
will stand thus, 

S. 670 E. } The third rule applies in this 
N. 28 E. I case. 
When the quantity of any angle in a survey is wanted, the 
preceding course must be reversed ; then both courses will run 
from the same point. 

Converging of Meridians. 

The breadth of a degree of longitude in any parallel of 
latitude is to the breadth of a degree upon the equator, as the 
Co-sine of that Lat. is to Radius. 

R. : 60 Miles : : Co-sine of the Lat. : the breadth of a degree 
on that Lat. 

As Radius - 10.00000 

Is to 60 Miles, - - 1.77815 
So is Co-sine Lat. 60O 9.69897 



11.47712 
10.00000 



To 30 Miles - 1.47712 



MISCELLANEOUS QUESTIONS. 

1. At a certain point I took the elevation of a tower 30 15' 
— then measured toward the tower on an angle of depression 
70 333 feet to a level with the base of the tower, when I took 
the elevation again 8°. — Required the height of the tower and 
the distance from the second place of observation to the base ; 
also how much higher the land was at the place of the first ob- 
servation than at the second. 

Am Height, - - - 99.6 feet. 

Distance required, - 708.6 feet. 

Difference in the height of land, 40.58 feet. 

2. Two persons made observations on the altitude of a me- 
teor, both being on the same side of it, and in a vertical plane 
passing through it. The distance of their stations were 200 
rods apart, and at one the angle of elevation was 36° 25^, at 
the other 32° 50', and at the last the outer limb of the meteor 



104 APPENDIX. 

subtended an angle of 2^. — Required the distance from the 
last place of observation, also the height and diameter of it. 

M, Q. R. 

Answer. — The distance, 5 .. 3 .. 60 
Height, 3 .. .. 70 

Diameter, 1 8 feet 2 inches. 

3. Fx'om tlie top of a steeple 165 feet high, the angle of depression of Che 
nearest bank of a river is 11° 15', that of the opposite bank is 6° 15'. Re- 
quired the width of the river. .insw. 41.13 rods. 

4. What length of cart-tire will it take to band a wheel 5 feet in diameter ? 

.Snsw. 15 feet 8 1-2 inches. 

5. A gentleman laid out a garden in a circle, containing one acre, one 
quarter, and one rod, with a gravelled v/alk on the outer side of it within 
the circle which took up twelve rods of ground. What is the diameter of 
the circle, and what is the width of the walk ? 

^nsw. The diameter 16 rods — Width of the walk 4 feet. 

6. Neptune laid out 1000 square miles of the surface of the sea in a circle, 
and sold to Aeolus all that part of It which lies without a concentric circle of 
one third of the diameter. What is the diameter, and how much was sold ? 

.Snsw. The diameter 35.68 miles. The quantity sold 888.92 square miles. 

7. A Farmer laid out an elliptical orchard, the longest diameter of which 
was 30 rods, and the shortest was 20 rods, and surrounded the same with a 
wall two feet thick, within the figure. What is the quantity within the wall, 
and how much is covered by it ? d. Q, R. 

Jinsio. Within the wall 'i .. 3 ..22 

Covered by the wall, 9.3 rods. 

8. From a point in an equilateral triangle, I measured the distances to each 
corner, and found them 20, 28, and 30 rods. Required the area and the 
length of the sides.* - .?- Q. R. 

Answ. The Area 5 .. 1 ..33 
Length of each side 45 rods. 

9. Required the dimensions of a parallelogram, containing one acre and 
a. half, bounded by 64 rods of fence. Answ. 12 by 20 rods. 

10. The area of a parallelogram is five acres one quarter and thirty-five 
rods, and the diagonal is forty-three rods. Required the length of the sides. 

Ansio. 35 by 25 rods. 

11. Required the dimensions of a parallelogram containing twenty-six 
acres one quarter and twenty-four rods, when the length exceeds the breadth 
by fifty-two rods. Ansiv, 44 by 96 rods. 

12. Required the dimensions of a parallelogram containing 250 acres, 
when the sides are in the proportion of 7 to 3. Ansio. 130.93 by 305 1-2. 

13. The state of Connecticut contains a little upwards of 4828 square 
miles, or 3,090,000 acres, including rivers, harbours, creeks, roads, &c. if 
this quantity of land is laid in a square, what will be the length of each 
side? M. Q. R. 

Answ. 69 .. 1 .. 75.11 



JVote. In the Preface, it is observed that the Traverse Table in this book 
h calculated for any distance up to 50. After the Preface was printed, it 
was thought best to extend that Table to 70. The table of Logarithms is 
filso much more extensive, than is noticed in the Preface. 

* This may be solved geometrically. 



I 



ERRATA. 

Appendix page 89, line 22, for "less" read legs. 

« " 94 line 25, for "from 2 to 1" read/rom 2 to <S', 
« " 98 line 33, for "columns" read column. 
« *' lOl line 25, for "raurstone,"read mecr.s^owe. 
l]|;f*'In the engraving on page 94 of the appendix, and oppo- 
site the second angle [near the figures l6i90) should have 
been inserted the figure 2 ; this deficiency can easily ^be sup? 
plied by the pen or pencil. 



MATHEMATICAL TABLES. 



VIZ: 



L A Table of Logarithms for Numbers. 
II. j3 Table of Logarithmic or Artificial Sines, Tangents, and 
Seca7its. 

III. A Traverse Table, or Table of Diff'erence of Latitude and 
Departure. 

IV. A Table of Natural Sines. 



I. A TABLE OF LOGARITHMS FOR NUMBERS. 

Logarithms are Numbers in Arithmetical Progression, corres» 
ponding to other Numbers in Geometrical Proportion. 
As, 0. 1. 2. 3. 4. Logarithms. 

1. 10. 100. 1000. 10000. Numbers. 

The Logarithm for any Number less than 10 is a certain 
number of Decimals ; for any Number between 10 and 100, 
it is 1 with Decimals ; for any Number between 100 and IOOO5 
it is 2 with Decimals, &.c. The whole Number in Logarithms, 
or the Number which stands at the left hand of the Decimal 
point, is called the Index ; and is always a unit less than the 
places of figures in the whole Number for which it is the Lo- 
garithm : Thus, 

The Log. of 6543 is 3.81578 

664.3 - 2.81578 

65.43 - ' 1.81578 
6.543 - 0.81578 

The Log. of a Decimal Fraction is the same as that of an 
Integer, only the Index is negative, and is distinguished from a 
positive one, by placing a Point, or a negative Sign before it ; 
Thus, 

The Log. of 0.6543 is .9.81578 or —1.81578. 

0.06543 - .8.81578 or— 2.81578. 

Note. — In the following Table the Index is not prefixed. It 
may be easily supplied as it is always a unit less than the number 
of figures in the corresponding natural whole number. ^ 

1 



2. LOGARITHMS. 

To find the Logarithm of any Number. 

If the Number is less than 100, its Log. is found in the first 
page of the Table, directly opposite thereto : Thus, the Log. 
of 34 is 1.53148. 

If the Number consists of three figures, find it in the first 
column of the following part of the Table, opposite to which, 
and under 0, is the Log, : Thus the Log. of 346 is .63908 to 
which prefix 2 for the Index, because there are three places of 
figures in the whole Number. 

If the given Number contains four figures, the first three are 
to be found, as before, in the side column, and under the fourth 
at the top of the table is the Log. to which the Index 3 is to be 
prefixed, if the given Number is an Integer : Thus the Log. of 
3467 is .53995 to which prefix 3 for the Index. 

If the given Number exceeds four figures, find the differ- 
ence between the Log. of the first four figures, and the next 
following Log. Multiply this difference by the remaining figure 
or figures in the given Number ; point off as many figures to 
the right hand as there are in the multiplier ; and the remain- 
der, added to the Log. of the first four figuros, will be the re- 
quired Log. 

To find the Number corresponding to any givcxi Logarithm. 

Find the next less Log. to that given in the column marked 
at the top, and continue the sight along that horizontal line, 
and the Log. the same as that gives, or very near it, will be 
found ; then the first three figures of the corresponding Num- 
ber will be found opposite, in tlie first side column, and the 
fourth figure directly above, at the top of the page. If the 
Index of the given Log. is 3, the four figures thus found are 
whole numbers ; if the Index is 2, the first three figures are 
whole numbers, and the fouri»h is a Decimal, and so on. 

To find the nearest number corresponding to any Log, for 
more than four figures, find the Log. next less than the given 
one, and take the difference between that and the given one; 
also take the difference between the next greater and the next 
less Log. than the given one ; divide the former difference by 
the latter, according to the Rule in Division of Decimals for 
dividing a less number by a greater ; add the Quotient to the 
number answering to the Log. next less than the given one, and 
you will have the required Number ; whether a whole, or a 
mixed Number will be determined by the Index. 

The addition and subtraction of Logarithms answers the 
came purpose as the multiplJQation and division of their corres- 



LOGARITHMS. 3 

ponding Numbers : That is, the Log. of any two Numbers- be- 
mg added, their sum will be the Log. of the Product of those 
Numbers ; and the Log. of one Number being subtracted from 
the Log. of another Number, the Remainder will be the Log, 
of the Quotient of one of those Numbers divided by the other. 
Again, the Log. of any Number being doubled will produce the 
Log. of the Square of that number ; and one half the Log. of 
any Number is the Log. of the Square Root of that Number. 



n. Of the Table of Logarithmic or Artijicial Sines, Tangents^ 
and Secants. 

.J^o find the Logarithmic Sine, S,'c.f6r any number of Degrees 
ilTid Minutes, within the compass of the Table. 

If the Degrees be less than 45, look for them at the top of the 
columns, and under Sine, Tangent or Secant, whichever is 
wanted, and for the Minutes at the left hand ; but if more than 
45, look for the Degrees at the bottom over Sine, &c. and for 
the Minutes at the right hand ; under or oyer the Degrees and 
against the Minutes will be the required Log. Sine, &c. 

To find the Degrees and Minutes corresponding to a given 
Logarithmic Sine, 4'C. 

Look in the proper column for the nearest-Log. to the given 
one ; and the Degrees and Minutes standing over or under anct 
against it, are those required. 

JS'ote. When the Log. Sine, &c. for more than 90*^ is re- 
quired, subtract the given number of Degrees from 180°, 
and make use of the Remainder. 

Tt will be observed that this Table is calculated only for every 
5 Minutes. This ^vas thought sufficient for Surveyors, as few 
Compasses will take a course to greater exactness. If, how- 
ever, a Question is to be solved where greater accuracy is re- 
quired, work by natural Sines. Or, 

'The Log. Sine, &,'C. for any Minute may he found as follows: 
Look in the Table for the Log. of the nearest number o.f 
Minutes greater than the given one, and from this subtract the 
next less Log. contained in the Table : Then say, as 5 Minutes, 
is to this difference ; So is the excess of the given Minutes 
above 5, 10, 16, 20, 25, &c. ; To a fourth number, which add 
to the Log. of the Minutes next less than the given number, and 
-'he sum will be the Log. required. 



LOGARITHMS. 

Example, 

Required the Logarithmic Sine of 34° 23' 

Sine of 34° 25' 9. 75221 

34 20 9.75128 



Difference 

As 5 : 93 : : 3 : 56 

Sine of 34° 20' 9.75128 

Add - . - 66 



Sine of 34° 23' 9.75184 



To find the nearest Minutes corresponding to a given Loga 
rithtnic Sine, 4'C. 

Look in the Table, in the proper column, for the Log. next 
less than the given one, and take the difference between that 
and the given one ; also take the difference between the next 
greater and the next less Log. than the given one ; Then say. 
As the latter difference ; is to 5 Minutes ; so is the former dif- 
ference ; to the number of Minutes to be added to the Minutes 
of the Log. next less than the given one. 

Example. 

Required the Degrees and Minutes corresponding to the Logarith- 
mic Tangen.t 9 J S597. 

Given Log, 9.73597 Next greater Log. 9.73627 
Next less 9.73476 Next less - 9.73476 



Difference 121 Difference 151 



As 151 : 5 : : 121 : 4 
The Degrees and Minutes for the Log. next less than the 
given one are 28° 30' to which add 4' and it makes 28° 34'. 

JVote. As after the most careful attention of the Printers 
some figures in the Table may be wrong ; and as some 
may be so blurred as to be illegible, let it be observed, 
that the Sines and Co-Secants, the Co-Sines and Secants, 
and the Tangents and Co-Tangents, standing against each 
other respectively, being added together, will amount to 
20.00000, if the Tables are accurate. Thus against 28*^ 
20' t^e Sine 9.67533 added to the Co-Secant 10,32367 



LOGARITHMS. £J 

their sum is 20.00000 ; so also is the sum of the Co-Sine 
9.94458 and the Secant 10.05542, and likewise the sum of 
the Tangent 9.73175 and the Co-Tangent 10.26825. An 
error may consequently be easily detected, or any defaced 
figure be supplied. 



To calculate the Northing or Southing, S,~c,for any Course and 
Distance by Logarithms . 

This is done by the first Case of Right Angled Trigonome- 
try, as follows : 

Pind the Log. Sine and Co-Sine of the Course ; to each of 
these add the Log. of the Distance ; subtract Radius or lO.OOOOC 
from their sums, and the remainders will be the Log. of the re 
quired Latitude and Departure. 

JVote. When the Angle is very small or very large, and the 
Distance short, the sum of the Log. Sine or Co-Sine and the 
Log. of the Distance may be less than 10.00000 or Radi- 
us, which cannot therefore be subtracted. In such caseg 
look for the Log. without regard to the Index, and the cor- 
responding number will be a Decimal, the first figure of 
which will be tenths if the Index be 9, and hundredths if 
the Index be 8. 



A TABLE OF LOGARITHMS. 



JSo. 1—100. 




Log;. 0.00000— 2.00000. j 


N. 


Log-. 


N. 


Log. 


N. 


Log. 


N. 
61 


Log. jN., Log. 
1.78533, Slj 1.90849 


1 


0.00060 


21 


1.32222 


41 


1.61278 


2 


0.30103 


22 


1.34242 


42 


1.6-2325 


62 


1.79239 82 1.91381 


i 3 


0.47712 


23 


1.36173 


43 


1.63347 


63 


1.79934 83! 1.91908 


4 


0.60206 


24 


1.38021 


44 


1.64345 


64 


1.80618 84i 1.92428 


5 


0.69897 


25 


1.39794 


45 


1.65321 


65 


1.81291 85 


1.9-2942 


6 


0.77815 


26 


1.41497 


46 


1.66276 


66 


1.81954 86 


1.93450 


7 


0.84510 


27 


1.43136 


47 


1.67210 


67 


1.82607 87 


1.93952 


8 


0.90309 


28 


1.44716 


48 


1.68124 


68 


1.83251 83 


1.9444S 


9 


0.95424 


29 


1.46240 


49 


1.69020 


69 


1.83885 89 


1.94939 


10 


1.00000 


30 


1.47712 


50 
51 


1.69897 


70 


1.84510 90| 1.95424) 


11 


1.04139 


31 


1.49136 


1.70757 


71 


1.85126 


91 


1.95904 


12 


1.07918 


32 


1.50515 


52 


1.71600 


72 


1.85733 


92 


1.96379 


13 


1.11394 


33 


1.51851 


53 


1.72428 


73 


1.86332 


93 


1.56848 


14 


1.14613 


34 


1.53148 


54 


1.73239 


74 


1.86923 


94 


1.97313 


15 


1.17609 


35 


1.54407 


o5 


1.74036 


75 


1.87506 


95 


1,97772 


16 


1.20412 


36 


1.55630 


56 


1.74819 


76 


1.88081 


96 


1.98227 


17 


1.2.3045 


37 


1.56820 


57 


1.75587 


77 


1.88649 


97 


1.98677 


18 


1.25527 


38 


1.57978 


58 


1.76343 


78 


1.89209 


98 


1.99123 


19 


1.27875 


39 


1.59106 


59 


1.77085 


79 


1.89763 


99 


1.99564 


20 


1.30103 40 


1.60206 60| 


1.77815 80 


1.90309 


100 


2.00000 



A TABLE OF LOGARITHMS, 




A TABLE OP LOGARITHMS. 



No. 1600— il-^TO. 


Log. 20412—34242. \ 




K0.| 


1 1 


2 3 1 4 1 


^ i 


6 1 7 1 


8 


9 


160 


20412 20439 


20466 2049.'! 


20520 


20548 20575,206021 


20629 


20656 




161 


0683, 0710 


0737 0763 


0790 


08171 


0844 


0871 


0898 


0925 




162 


0952 097S 


1005 1032 


1059 


10851 


1112 


1139 


1165 


1192 




163 


1219; 1245 


1272 1299 


1325 


1352, 


1378 


1405 


1431 


1158 




164 


1484 1511 


1537 1564 15901 


I6I7; 


164:^ 


1669 


1696 


1722 




165 


17481 1775 


1801 1827 


1854 


1380; 


1906 


1932 


1958 


1985 




166 


2011! 2037 


2063 2069 


2115 


2141: 


2167 


2194 


2220 


2246 




167 


2272' 2298 


2324 2356 


2376 


2401, 


24:: 


2453 


247S 


2505 




168 


253r 2557 


2583 2608 


2634 


2660, 


2686 


2712 


2737 


2763 




169 

no 


2789; 2814 
3045. 3070 


2840 2866 
3096 3121 


2891 


29)7 
3172 


2943 
3198 


2966 


2994 


3019 




3147 


3223 


3-249 


3274 




171 


3300 3325 


3350 3376 


3401 


3426 


3452 


3477 


3502 


3528 




172 


3553 3578 


3603 3629 


3854 


3679 


3704 


3729 


3754 


3779 




173 


3805 3830 


3855 3SS0 


3905 


3930 


3955 


3980 


4005 


4030 




174 


4055' 4080 


4105 41:30 


4155 


4180 


4-2ai 


4228 


4254 


4279 




175 


4304; 4329 


4353 4378 


4403 


4428 


445-J 


4477 


4502 


4527 




176 


4551; 4576 


4601 46-25 


4650 


4674 


460!:. 


4724 


4748 


4773 




177 


4797. 4822 


4846 4871 


4895 


4920 


494-: 


4989 


4993 


5018 




17S 


5042; 5066 


5091 5115 


5139 


5164 


51SS 


5212 


5237 


5261 




179 

180 


5285! 5310 
55271 5551 


5334 5358 
5575 5600 


5382 


5406 

5648 


5431 

5672 


5455 


5479 


5503 




5G24 


5-396 


5720 


5744 




181 


5768 5792 


5815 584(3 


5864 5888 


5912 


5935 


5959 


5983 




182 


6007 6031 


6055 6079 


6102 


'6126 


6150 


6174 


6198 


6221 




183 


6245 6269 


6293 6316 


6340 


6364 


6387 


6411 


6435 


6458 




184 


6482 


6505 


6529 6553 


6576 


6600 


6623 


6647 


6670 


6694 




185 


6717 


6741 


6764, 6788 


6811 


6334 


685S 


6881 


6905 


6928 




186 


6951 


6975 


6998' 7021 


7045 


7068 


7091 


7114 


7138 


7161 




187 


7184 


7207 


7231 1 7254 


7277 


730C 


7323 


7346 


7370 


7393 




188 


7416 


7439 


7432i 7485 


75CS 


7531 


7554 


7577 


7600 


7623 




189 
190 


7646 


7669 


7692! 7715 
7921; 7944 


7738| 7761| 


7784 


7807 


783i. 


7852 




7875 


7898 


7967 


7989 


6012 


8036 


8058 


8081 




191 


8103 


8126 


8149' 8171 


8194 


8217 


8240 


8262 


8285 


8307 




192 


8330 


8353 


8375' 8398 


8421 


8443 


6466 


8488 


8511 


6533 




193 


8556 


8578 


8601 S623| 8646 


8668 


8691 


8713 


8735 


8758 




194 


8780 


8803 


8825' 8847) 8870 


8892 


8914 


8937 


8959 


8981 




1951 9003 


9026 


9048' 9070 9092i 9115 


9137 


9159 


9161 


9203 




196 9226 


9248 


92701 9292 93141 9336 


9358: 938C 


9403' 9425 




197i 9447 


9469 


9491' 9513- 9535! 9557 


-9579 9G01 


9623' 9645' 




198' 9667 


9688; 9710' 9732i 9754i 9T76J 


9798 9820 


9842 9863 




199: 9835 
200 30103 


9907 


99291 9951; 99731 9994; 


i0016 3CC3& 
0233 0256 


30060 30081 
0276 0276 




30125 


30148 30168 30190 30211 1 




2011 0320 


0341 


0364 


0384' 0406, 042S 


0449 0^171 


0492; 0514 




202; 0535 


0557 


0578 


0600; 06211 0643 


0664' 0685 


0707 


072^ 




203| 0750 


07711 0792 


C8I4' 0835 


0856 


0678 0899 


0920 


0942 




204, 0963 


0984 


1006 1027 1048 


1069 


1091! 1112 


1133 


1154 




205 1175 


1197 


1218 1239 1260 


1281 


1302 1323 


1345 


1366 




206; 1367 


1408 


1429 1450 1471 


1492 


1513 1534 


1-555 


1576 




207| 1597 


1618 


1639 


1660' 1681 1 1702 


1723: 174J 


1765 


1785 




206 1806 


1827 


1846 


1869; ISOOI 1911 


1931. 1952 


1973 


1994 




209; 2015 
210 2222 


2035 


2056 


2077| 209a 


1 2118 


2139 2160 
2348 2366 


2181 


2-201 




2243 


I 2263 


22841 2305 


2325 


238- 


2406 




211 2428 


2449; 2469 


2490 


251C 


2531 


2552 2572 


2593 


2613 




212 2634 


2654 2675 


2695 


2715 


2736 


2756 277* 


2797 


2818 




213, 2838 


2858 2879 


2699 


291S 


2940 


2960 298C 


3001 


3021 




214, 3041 


3062 3082 


310-2 


3122 


3143 


3163 3183 


3203 


3224 




2L 


> 3244 


3264 3284 


330J 


332c 


3345 


3365 S38fi 


3405 


3425 




21* 


5 344i 


346. 


) 3486 


350f 


3526 3546 


3566 3586 


3606 


3626 




21 


- 364C 


366( 


) 3686 


370e 


3726 3746 


3766 3786 


3806 


3826 




218 3846 


386( 


) 3885 


390. 


. 3925 3945 


3965 396c 


400c 


4025 




219 4044 


406- 


! 4' 84 


410' 


I 41-24 4143 


4163 418i 


4203 


4223 




NO. 


1 


2 


3 


4 i 5 


6 1 7 


8 


9 





A TABLE OF LOGARITHMS. 



No. 2200—2800. Log. 34ii42— 44716. ( 


NO. 





1 


2 


3 


4 . 5 


6 


7 1 8 i 9 1 


220 


34242 


34262 


34282 


34301 


34321 34341 


34361 


34380 34400 3442CJ 


221 


4439 


4459 


4479 


4498 


4518 4537 


4557 


4377 


4396 


4616 


i22 


4635 


4655 


4674 


4694 


4713 4733 


4753 


4772 


4792 


4811 


223 


4830 


4850 


4869 


4889 


4903 4928 


4947 


4967 


4986 


5005 


224 


5025 


5044 


5064 


5083 


5102 5122 


5141 


3160 


5180 


619£ 


225 


5218 


5238 


5257 


5276 


5295 5315 


5334 


5353 


5372 


5392 


226 


5411 


5430 


5449 


5468 


5488 5507 


3526 


5545 55641 


6583 


227 


5603 


5622 


5641 


5660 


5679 5698 


5717 


3736 


3735 


3774 


228 


5793 


5813 


5832 


5851 


5870 


5889 


5908 


5927 


5946 


5966 


229 
230 


5984 


6003 


6021 
6211 


6040 
6229 


6059 


6078 


6097 


6116 


6133 


6154 


6173 


6192 


6248 


6267 


6286 


6305 


6324 


6342 


231 


6361 


6380 


6399 


6418 


6436 


6455 


6474 


6493 


6311 


6530 


232 


6549 


6568 


6586 


6605 


6624 


6642 


6661 


6680 


6698 


6717 


233 


6736 


6754 


6773 


6791 


6810 


6829 


6847 


6866 


6884 


6903 


234 


6922 


6940 


6959 


6977 


6996 


7014 


7C33 


7051 


7070 


7088 


235 


7107 


7125 


7144 


7162 


7181 


7199 


7218 


7236 


7234 


7273 


236 


7291 


7310 


7328 


7346 


7365 


7383 


7401 


7420 


7438 


7457 


237 


7475 


7493 


7511 


7530 


7548 


7666 


7585 


7603 


7621 


7638 


238 


7658 


7676 


7694 


7712 


7731 


7749 


7767 


7785 


7803 


7822 


239 
240 


7840 


7858 


7876 


7894 


7912 


7931 
8112 


7949 


7967 


7985 8003 
8166j 8184 


8021 


8039 


8057 


8075 


8093 


8130 


8148 


241 


8202 


8220 


8238 


8256 


8274 


8292 


8310 


8328 


83461 8364 


242 


8382 


8399 


8417 


8433 


8453 


8471 


8489 


85071 8525J &543 


243 


8561 


8578 


8596 


8614 


8632 


8650 


8668 


8686 87031 8721 


244 


8739 


8757 


8775 


8792 


8810 


8828 


8846 


8863 88811 8899 


245 


8917 


8934 


8952 


8970 


8987 


9005 


9023 


9041 9038; 9076 


246 


9094 


9111 


9129 


9146 


9164 


9182 


9199 


9217 9233! 9252 


247 


9270 


9287 


9305 


9322 


9340 


9358 


9375 


9393 9410 9428 


248 


9445 


9463 


9480 


9498 


9515 


9533 


9550 


9568 9585 9602 


249 


9620 


9637 


9655 


9672 


9690 


9707 
9881 


9724 


9742 9739 9777 
99151 99331 9950 


250 


9794 


9811 


9829 


9846 


9863 


9898 


251 


9967 


9985 


40002 


40019 


40037 


40054 


40071 


40088:40106:40123 
02611 02781 0295 


232 


4D140 


40157 


0175 


0192 


0209 


0226 


0243 


253 


0312 


0329 


0346 


0364 


0381 


0398 


0'415 


04321 0449 


0466 


254 


0483 


0500 


0518 


0535 


0552 


0569 


0588 


0603J 0620 


0637 


255 


0654 


0671 


0688 


0705 


0722 


0739 


0756 


0773! 0790 


0807 


256 


0824 


084l 


0858 


0875 


0892 


0909 


0926 


0943 0960 


0976 


257 


0993 


1010 


1027 


1044 


1061 


1078 


1095 


1111 1128 


1145 


258 


1162 


1179 


1196 


1212 


1229 


1246 


1263 


1280 1296 


1313 


259 
260 


1330 


1347 


1363 


1380 


1397 


1414 


1430 


1447 1 1464 


1481 


1497 


1514 


1531 


1547 


1564 


1581 


1597 


1614! 1631 


1547 


261 


1664 


1881 


1697 


1714 


1731 


1747 


1764 


1780 


1797 1814 


262 


1830 


1847 


1863 


1880 


1896 


1913 


1929 


1946 


19631 19791 


263 


1996 


2012 


2029 


2045 


206? 


2078 


2095 


2111 


2127 


2144 


264 


2160 


2177 


2193 


2210 


2226 


2243 


2259 


2275 


2292 


2308 


265 


■2325 


2341 


2357 


2375 


2390 


2406 


2423 


2439 


2455 


2472 


266 


2488 


2504 


2521 


2537 


2553 


2570 


2586 


2602 


2619 


2635 


267 


2651 


2667 


2684 


2700 


2716 


2732 


2749 


2765 


2781 


2797 


268 


2813 


2830 


2846 


2862 


2878 


2894 


2911 


2927 


29431 2959! 


26e 
270 


2975 


2991 


3008 
3169 


3924 


3040 


3056 

3217 


3072J 3088: 3104 


3120 


3136 


3152 


3185 


3201 


3233: 3249 


3263 


3281 


271 


3297 


3313 


3329 


3345 


3361 


3377 


3393 


3409 


3425 


3441 


272 


3^157 


3473 


1 3489 


3505 


3521 


3537 


3553 


3569 


3584 


3600 


273 


3616 


3632 


36481 3664 


3680 


3696 


3712 


3727 


3743 


3759 


274 


3775 


3791 


3807 


3823 


3838 


3854 


3870 


3886 


3902 


3917 


275j 3933 


394? 


3965 


3981 


3996 


4012 


4028 


4044 


4059 


4075 


27f 


4091 


410- 


4122 


4138 


4154 


4170 


4185 


4201 


4217 


4232 


,27' 


n 4248 


4264 


4279 


4293 


4311 


4326 


43^12 


4358 


4373 


4389 


27f 


i 4404 


442C 


4436 


4451 


4467 


4483 


4498 


4514 


4529 


4545 


Hi 


) 456C 


457e 


4592| 4607 


4623 


4638 


4654 


4669 


4685 


4700 


no 





1 


2 i 3 


4 


5 


6 


7 


8 


p 



A TABLE OF LOGARITHMS. 



No. £800—3400. Log. 44716—53148. \ 


so 

■28f 





1 


2 
44747 


3 


4 


5 


6 1 7 


8 


9 

44856 


44716 


44731 


44762 


44778 


44793 


44809 


44824 


44840 


■281 


4871 


48S6 


4902 


4917 


4932 


4948 


4933 


4979 


4994 


5010 


•282 


5025 


5040 


5056 


507] 


5086 


5102 


5117 


5133 


5148 


5163 


283 


.5179 


5194 


5209 


5225 


6240 


5255 


5271 


5286 


5301 


5317 


284 


5332 


5347 


6362 


5378 


5393 


5408 


5423 


5433 


5454 


5469 


285 


5484 


6500 


5515 


5530 


5545 


5561 


5576 


5531 


5606 


5621 


28fi 


5637 


5652 


5637 


5682 


5697 


5712 


5728 


5743 


5758 


5773 


287 


5788 


5803 


5813 


5834 


5849 


5834 


5879 


5894 


5908 


5924 


288 


5939 


5954 


5963 


598^ 


6000 


6015 


6030 


6045 


6060 


6076 


289 
290 


6090 


6105 


6120 


6135 


6150 


6165 


6180 


6135 


8210 


6225 


6240 


6255 


6270 


6285 


6300 


6315 


6330 


6:345 


6359 


6374 


291 


6389 


6404 


6419 


6434 


6449 


6464 


6479 


6434 


6509 


6523 


292 


6538 


6553 


6568 


6583 


6598 


6613 


6627 


6642 


6657 


667^ 


29E 


6687 


6702 


6716 


6731 


6746 


6761 


6776 


6790 


6805 


682C 


294 


6835 


6850 


6864 


687f* 


6894 


6909 


6323 


6938 


6953 


6967 


295 


3982 


6997 


7012 


7026 


7041 


7056 


7070 


7085 


7100 


7114 


296 


7129 


7144 


7159 


7173 


7188 


7202 


7217 


7232 


7246 


7261 


297 


7273 


7290 


7305 


7319 


7334 


7349 


7363 


7378 


7392 


7407 


233 


7422 


743S 


7451 


7435 


7480 


7494 


7503 


7524 


7538 


7553 


299 
;300 


7567 
7712 


7582 


7538 


7311 

7756 


7625 


7640 


7654 


7669 
7813 


7683 


7698 


7727 


7741 


7770 


7784 


7799 


7828 


7842 


301 


7857 


7871 


7885 


7900 


7914 


7929 


7943 


7958 


7972 


798q 


302 


8001 


8015 


8029 


8044 


8058 


8073 


8087 


8101 


8116 


8I3C 


303 


8144 


8159 


8173 


8187 


8202 


8216 


8230 


8244 


8259 


8273 


304 


8287 


8302 


8316 


8330 


8344 


8359 


8373 


8387 


8401 


8416 


305 


8430 


8444 


8458 


8473 


8487 


8501 


8515 


8530 


8544 


8558 


306 


8572 


8586 


8601 


8615 


8829 


86-13 


8657 


8671 


8686 


870C 


307 


8714 


8728 


8742 


8756 


8770 


8785 


8799 


8813 


8827 


8841 


308 


8855 


8869 


8883 


8837 


8911 


8926 


8940 


8954 


8968 


8982 


309 
310 


8996 


9010 


3024 
9164 


903S 
9178 


9052 


9066 


9080 
9220 


9094 


9108 


9122 


9136 


9150 


9192 


9206 


9234 


3248 


9262 


311 


9276 


9290 


9304 


9318 


9332 


9346 


9360 


9374 


9388 


9402 


312 


9415 


9429 


9-143 


9457 


9471 


9485 


3499 


3513 


9527 


9541 


313 


9554 


9568 


9582 


9593 


9810 


9624 


9638 


9651 


9665 


9679 


314 


9693 


9707 


9721 


9734 


9743 


9762 


9776 


9790 


9803 


9817 


315 


9831 


9845 


9859 


9872 


9888 


9900 


9914 


9927 


3941 


9955 


316 


9969 


9982 


9996 


50010 


50024 


50037 


50051 


5?j85 


50079 


50092 


317 


50106 


50120 


50133 


0147 


0161 


0174 


0188 


0202 


0215 


0229 


318 


0-243 


0256 


0270 


02S4 


0297 


0311 


0325 


0338 


0352 


0365 


319 

320 


0379 


0393 


0406 
0542 


0420 
0556 


0433 

0569 


0447 


0461 
0598 


0474 


0488 


0501 


0515 


0529 


0583 


0610 


0623 


0637 


321 


0651 


0334 


0378 


0391 


0705 


0718 


0732 


0745 


0759 


0772 


322 


0786 


0799 


0813 


0823 


0840 


0853 


0866 


0880 


0893 


0907 


3-23 


0920 


0934 


0947 


0931 


0974 


0987 


IC-Ol 


1014 


1028 


1041 


324 


1055 


lOGS 


1081 


1005 


1108 


1121 


1135 


1148 


1162 


1175 


325 


1188 


1203 


1215 


1228 


1242 


1255 


1268 


1282 


1295 


1308 


i'>6 


1322 


1335 


"1348 


1362 


1375 


1388 


1402 


1415 


1428 


1441 


327 


1455 


1468 


1481 


1495 


1508 


1521 


1534 


1548 


1561 


1574 


328 


1587 


1601 


1614 


1627 


1640 


1654 


1637 


1680 


1693 


1706 


329 
330 


1720 


1733 


1746 


1759 

1891 


1772 


1786 


1799 


1812 


1825 


1838 


1851 


1865 


1878 


1904 


1917 


1930 


1943 


1957 


1970 


331 


1983 


1996 


2009 


2022 


2035 


2048 


2031 


2075 


2088 


2101 


332 


2114 


2127 


2140 


2153 


2166 


2179 


2192 


2205 


2218 


2231 


333 


2244 


i'257 


2270 


2284 


2297 


2310 


2323 


2336 


0349 


2362 


334 


2375 


2388 


2401 


i414 


2427 


2440 


2453 


2466 


^9 


2492 


'^Sj 


2504 


2517 


2530 


2543 


2556 


2539 


2582 


2595 


2608 


2621 


336 


2634 


2647 


2360 


2673 


2686 


2699 


2711 


2724 


1737 


2750 


337 


2763 


2776 


2789 


2802 


2815 


2827 


2840 


2653 


ifS66 


2879 


338 


i>892 


2905 


2917 


2930 29431 


2956 


2969 


2982 


2991 


3007 


339 


3020 


3033 


3046 


3058 


3071 
4 


3084 


3097 


3110 

7 


3122 3135J 


NO. 


d 


1 


2 


3 


5 


6 


8 1 


9 1 



10 



A TABLE OF LOGARITHMS. 



No. 3460—4000. Log. 53148—60206." | 


NO. 

340 





1 


2 


3 


4 


5 


6 


7 


8 
53250 


9 


53148 


63161 


53173 


53186 


63199 


53212 


53224 


53237 


53263 


341 


3275 


3288 


3301 


3314 


3326 


3339 


3362 


3364 


3377 


3390 


-3i9. 


3403 


3415 


3428 


3441 


3453 


3466 


3479 


3491 


5504 


3517 


343 


3529 


3542 


3655 


3567 


3580 


3593 


3605 


3618 


3631 


3643 


344 


3656 


3668 


3681 


3694 


3706 


3719 


3732 


3744 


3757 


3769 


345 


3782 


3794 


3807 


3820 


3832 


3845 


3857 


3870 


3882 


3895 


346 


3908 


3920 


3933 


3945 


3958 


3970 


3983 


3995 


4008 


4020 


347 


4033 


4045 


4058 


4070 


4083 


4095 


4108 


4120 


4133 


4145 


348 


4158 


4170 


4183 


4195 


4208 


4220 


4233 


4246 


4258 


4270 


349 
350 


4283 
4407 


4296 
4419 


4307 


4320 


4332 


4345 


4357 


4370 


4382 


4394 


4432 


4444 


4456 


4469 


4481 


4494 


4506 


4518 


351 


4531 


4543 


4555 


4568 


4580 


4593 


4605 


4617 


4630 


4642 


352 


4654 


4667 


4679 


4691 


4704 


4716 


4728 


4741 


4753 


4765 


353 


4777 


4790 


4802 


4814 


4827 


4839 


4851 


4864 


4876 


4888 


354 


4900 


4913 


4925 


4937 


4949 


4962 


4974 


4986 


4998 


5011 


355 


5023 


6035 


6047 


5060 


5072 


5084 


5096 


5108 


5121 


6133 


356 


5145 


5157 


5169 


5182 


5194 


6206 


5218 


6230 


5242 


5255 


357 


5267 


5279 


5291 


6303 


5315 


5328 


5340 


5352 


5364 


5376 


358 


5388 


5400 


5413 


5426 


5437 


5449 


5461 


6473 


5485 


5497 


359 
360 


5509 
5630 


5622 
6642 


6534 


5546 
6666 


5558 


5670 


5582 


6594 


5606 


5618 


6654 


6678 


5691 


6703 


6715 


5727 


5739 


361 


5751 


5763 


5775 


5787 


5799 


5811 


6823 


6835 


5847 


5859 


362 


5871 


6883 


5895 


5907 


5919 


6931 


6943 


5965 


6967 


5979 


363 


5991 


6003 


6015 


6027 


6038 


6060 


6062 


6074 


6086 


6098 


364 


6110 


6122 


6134 


6146 


6158 


6170 


6182 


6194 


6205 


6217 


365 


6229 


6241 


6253 


6265 


6277 


6289 


6301 


6312 


6324 


6336 


366 


6348 


6360 


6372 


6384 


6396 


6407 


6419 


6431 


6443 


6455 


367 


6467 


6478 


6490 


6502 


6514 


6526 


6638 


6549 


6561 


6573 


368 


6586 


6697 


6608 


6620 


6632 


6644 


6656 


6667 


6679 


6691 


369 

370 


6703 


6714 

6832 


6726 
6844 


6738 


6750 


6761 


6773 
6891 


6785 


6797 


6808 


6820 


6855 


6867 


6879 


6902 


6914 


6926 


371 


6937 


6949 


6961 


6972 


6984 


6996 


7008 


7019 


7031 


7043 


372 


7054 


7066 


7078 


7089 


7101 


7113 


7124 


7136 


7148 


7159 


373 


7171 


7183 


7194 


7206 


7217 


7229 


7241 


7252 


726^ 


7276 


374 


7287 


7299 


■7310 


7322 


7334 


7345 


7357 


7368 


7380 


7392 


376 


7403 


7415 


7426 


7438 


7449 


7461 


7473 


7484 


7496 


7507 


376 


7519 


7630 


7542 


7563 


7666 


7576 


7588 


7600 


7611 


7623 


377 


7634 


7646 


7657 


7669 


7680 


7692 


7703 


7715 


7726 


7738 


378 


7749 


7761 


7772 


7784 


7795 


7B07 


7818 


7830 


7841 


7852 


379 
38C! 


7864 
7978 


7875 


7887 
8001 


7898 


7910 


7921 


7933 


7944 


7955 


7967 


7990 


8013 


8024 


8036 


8047 


8058 


8070 


8081 


381 


8092 


8104 


8115 


8127 


8138 


8149 


8161 


8172 


8184 


8195 


382 


8206 


8218 


8229 


8240 


8262 


8263 


8274 


8286 


8297 


8309 


383 


8320 


8331 


8345 


8354 


8365 


8377 


8388 


8399 


8410 


8422 


384 


8433 


8444 


8466 


8467 


8473 


8490 


8501 


8512 


8524 


8535 


385 


8546 


8557 


8569 


8580 


8591 


8602 


8614 


8625 


8636 


8647 


386 


8659 


8670 


8681 


8692 


8704 


8715 


8726 


8737 


8749 


8760 


387 


8771 


8782 


8794 


8805 


8816 


8827 


8838 


8850 


8861 


8872 


388 


8883 


8894 


8906 


8917 


8928 


8939 


8950 


8961 


8973 


8984 


389 
390 


8995 


9006 


9017 


9028 
9140 


9040 


9061 


9062 


9073 


9084 


9095 


9106 


9118 


9129 


S151 


9162 


9173 


9184 


9195 


9207 


391 


9218 


:9229 


9249 


9251 


9262 


9273 


9284 


9295 


9306 


9318 


392 


9329 


9340 


9.351 


9362 


9373 


9384 


9395 


9406 


9417 


9428 


393 


9439 


9450 


9461 


9472 


9483 


9494 


9506 


9517 


9528 


9539 


394 


9650 


9561 


9572 


9583 


9594 


9605 


9616 


9627 


9638 


9649 


395 


9660 


9671 


9682 


9693 


9704 


9715 


9726 


9737 


9748 


9759 


396 


9770 


9780 


9791 


9802 


9813 


9824 


9835 


9846 


9857 


9868 


397 


9879 


9890 


9901 


9912 


9923 


9934 


9945 


9956 


9966 


9977 


398 


9988 


9999 


60010 


60021 


60032 


60043 


60054 


60065 


60076 


60086 


399 

NO. 


60097 


60108 


0119 


0130 


0141 


0162 


0163 


0173 


0184 


0195 





1 


2 


3 


4 


5 


6 7 


8 


9 / 



A TABLE OF LOGARITHMS. 



II 



No. 4000—4600.- Log. 60206—66276. | 


NO. 





1 2 


3 


4 


5 


6 7 


8 9 


400 


60206 


60217 80228 


60239 


60249 


60260 


60271 60282 


60293 60304 


401 


0314 


0325 0336 


0347 


0358 


0369 


0379 0390 


0401 


0412 


402 


0423 


0433 


0444 


0455 


0466 


0477 


0487 


0498 


0609 


052C 


403 


0531 


0541 


0552 


0563 


0574 


0584 


0595 


0606 


0617 


0627 


404 


0638 


0649 


0660 


0670 


0681 


0692 


0703 


0713 


0724 


0735 


405 


0746 


0756 


0767 


0778 


0788 


0799 


0810 


0821 


0831 


0842 


406 


G853 


0863 


0874 


0885 


0895 


0906 


0917 


0927 


0938 


0948 


407 


0959 


0970 


0981 


0991 


1002 


1013 


1023 


1034 


1045 


1055 


408 


1066 


1077 


1087 


1098 


1109 


1119 


1130 


1140 


1151 


1162 


409 
410 


1172 


1189 
1289 


1194 
1300 


1204 


1215 
1321 


1225 


1236 
1342 


1247 
1352 


1257 


1268 
1374 


1278 


1310 


1331 


1363 


411 


1384 


1395 


1405 


1416 


1426 


1437 


1448 


1458 


1469 


1479 


412 


1490 


1500 


1511 


1521 


1532 


1642 


1553 


1663 


1574 


1684 


413 


1595 


1606 


1616 


1627 


1637 


1648 


1658; 1669 


1679 


1690 


414 


1700 


1711 


1721 


1731 


1742 


1752 


1763 


1773 


1784 


1794 


415 


1805 


1815 


1826 


1836 


1847 


1857 


1868 


1878 


1888 


1899 


416 


1909 


1920 


1930 


1941 


1951 


1962 


1972 


1982 


1993 


2003 


417 


2014 


2024 


2034 


2045 


2055 


2066 


2076 


2086 


2097 


2107 


418 


2118 


2128 


2138 


2149 


2169 


2170 


2180 


2190 


2201 


2211 


419 
420 


/'2221 
2325 


2232 


2242 


2252 


2263 


2273 

2377 


2284 
2387 


2294 
2397 


2304 


2315 


2335 


2346 


2356 


2366 


2408 


2418 


421 


2428 


2439 


2449 


2459 


2469 


2480 


2490 


2500 


2511 


2521 


422 


2531 


2542 


2552 


2662 


2572 


2583 


2693 


2603 


2613 


2624 


423 


2634 


2644 


2655 


2665 


2675 


2685 


2696 


2706 


2716 


2726 


424 


2737 


2747 


2757 


2767 


2778 


2788 


2798 


2808 


2818 


2829 


425 


2839 


2849 


2859 


2870 


2880 


2890 


2900 


2910 


£32] 


2931 


426 


2941 


2951 


2961 


2972 


2982 


2992 


3U0Z 


3012 


3022 


3033 


427 


3043 


3053 


3063 


3073 


3083 


3094 


3104 


3114 


3124 


3134 


428 


3144 


.3155 


3165 


3176 


3185 


3195 


3205 


3215 


3225 


3236 


429 
430 


3246 


3256 


3266 


3276 


3286 


3296 


3306 


3317 


3327 


3337 


3347 


3357 


3367 


"3377 


3387 


3397 


3407 


3417 


3428 


3438 


431 


3448 


3458 


3468 


3478 


3488 


3498 


3608 


3518 


3628 


3538 


432 


3.548 


3558 


3568 


3579 


3589 


3599 


3609 


3619 


362S 


3639 


433 


3649 


3659 


3669 


3679 


3689 


3699 


3709 


3719 


372S 


3739 


434 


3749 


3759 


3769 


3779 


3789 


3799 


3809 


3819 


382£ 


3839 


435 


3849 


3859 


3869 


3879 


3889 


3899 


3909 


3919 


392£ 


3939 


436 


3949 


3959 


3969 


3979 


3988 


3998 


4008 


4018 


4028 


4038 


437 


4048 


4058 


4068 


4078 


4088 


4098 


4108 


4118 


4128 


4137 


438 


4147 


4157 


4167 


4177 


4187 


4197 


4207 


4217 422' 


4237 


439 
44a 


4246 
4345 


4256 


4266 


4276 


4286 


4296 
4395 


4306 


4316 4326 


4335 
4434 


4355 


4365 


4375 


4385 


4404 


44141 4424 


441 


4444 


4454 


4464 


4473 


4483 


4493 


4603 


4513 


4525 


4532 


442 


4542 


4552 


4562 


4572 


4582 


4691 


4601 


4611 


462: 


4631 


443 


4640 


4650 


4660 


4670 


4680 


4689 


4699 


4709 


471S 


4729 


444 


4738 


4748 


4758 


4768 


4777 


4787 


4797 


4807 


4816 


4826 


445 


4836 


4846 


4856 


4865 


4876 


4885 


4896 


4904 


4914 


4924 


446 


49.33 


4943 


4953 


4963 


4972 


4982 


4992 


5002 


5011 


5021 


447 


6031 


6040 


5050 


5060 


6070 


5079 


6089 


5099 


5108 


6118 


448 


51 2P 


5137 


5147 


5167 


5167 


5176 


5186 


5196 


620S 


6215 


449 
450 


5225 


5234 


5244 
T341 


6254 


5263 
5360 


5273 


6283 


5292 


5302 


5312 


5321 


5331 


6350 


5369 


6379 


5389 


5398 


6408 


451 


.541 P 


5427 


5437 


5447 


5456 


5466 


6476 


6486 


6495 


5604 


452 


5514 


5523 


5532 


5543 


6552 


5562 


6571 


5581 


5591 


5600 


453 


561C 


5619 


5629 


6639 


5648 


5658 


5667 


5677 


5686 


5696 


454 


570e 


5715 


5725 


5734 


5744 


5753 


5763 


5772 


5782 


5792 


455 


580; 


5811 


5820 


6830 


5839 


5849 


5858 


5868 


5877 


5887 


456 


589t 


5906 


5916 


6926 


5935 


5944 


5954 


5963 


6973 


5982 


457 


5992 


6001 


6011 


6020 


6030 


6039 


6049 


6068 


6068 


6077 


458 


608- 


6096 


6106 


6115 


6124 


6134 


6143 


61,53 


6162 


6172 


45S 

\'0 


6181 


6191 


6200 


6210 


6219 


6229 
6 


6238 
6 


6247 
7 


6257 


6266 





1 


2 


3 


4 


8 


9 



12 



A TABLE OF LOGARITHMS. 



Nn 4f00 ^(^ 




Log 


6627 


5 71600 1 




VB 




NO. 

460 





1 


2 


3 


4 


5 


6 7 
86332 66342 


8 
66351 


9 


66276 


66285 


66295 


66304 


66314 


66S23 


66361 


461 


6370 


6380 


6389 


6398 


6408 


6417 


6427, 


6436 


6445 


6455 


462 


6464 


C474 


6483 


6492 


6502 


6511 


65211 


6530 


6539 


6549 


463 


6558 


6567 


6577 


6586 


6596 


6605 


6614, 


6624 


6633 


6642 


464 


6652 


6661 


6671 


6680 


6689 


6699 


6708 


6717 


6727 


6736 


465 


6745 


6755 


6764 


6773 


6783 


6792 


68011 


6811 


6820 


6829 


466 


6839 


6848 


6857 


6867 


6876 


6885 


6894 


6904 


6918 


6922 


467 


6932 


6941 


6950 


6960 


6969 


6978 


6987 


6997 


7006 


7016 


468 


7025 


7034 


7043 


7052 


7062 


7071 


7080 


7089 


7099 


7108 


469 
470 


7117 


7127 


7136 


7145 


7154 


7164 
7256 


7173 


7182 


7191 


7201 


7210 


7219 


7228 


7237 


7247 


7265 


7274 


7284 


7293 


471 


7302 


7311 


7321 


7330 


7339 


734R 


73571 


7367 


7376 


7385 


472 


7394 


7403 


7413 


7422 


7431 


7440 


7449 1 


7459 


7468 


7477 


473 


7486 


7495 


7504 


7514 


7523 


7532 


7541 


7650 


7560 


7569 


474 


7578 


7587 


7596 


7605 


7614 


7624 


7633| 


7642 


7651 


7660 


475 


7669 


7679 


7688 


7697 


7708 


7715 


7724 


7733 


7742 


7752 


476 


7761 


7770 


7779 


7788 


7797 


7806 


7815 


7825 


7834 


7843 


477 


7852 


7861 


7870 


7879 


.7888 


7897 


7906 


7916 


7925 


7934 


478 


7943 


7952 


7961 


7970 


7979 


798S 


7997 


8006 


8015 


8024 


479 
480 


8034 

8124 


8043 


8052 


8061 


8070 


8079 


8088 1 


8097 


8106 


8115 


8133 


8142 


8151 


8160 


8169 


8178 


8187 


8196 


8205 


481 


8215 


8224 


8233 


8242 


8251 


8260 


8269 


8278 


8287 


8296 


482 


8305 


8314 


8323 


8332 


8341 


8350 


8359 


8368 


8377 


8386 


483 


8395 


8404 


8413 


8422 


8431 


8440 


8449 


8458 


8467 


8476 


484 


8485 


8494 


8502 


8511 


8520 


8529 


8538 


8547 


8556 


8565 


485 


8574 


8583 


8592 


8601 


■8610 


8619 


8628 


8637 


8646 


8655 


486 


8664 


8673 


8681 


8690 


8699 


8708 


8717 


8726 


8735 


8744 


487 


8753 


8762 


8771 


8780 


8789 


8797 


8806 


8815 


8824 


8833 


488 


8842 


8851 


8860 


8869 


8878 


8886 


8895 


8904 


8913 


8922 


489 
490 


8931 


8940 


8949 


8958 


8966 


8975 
~9C6l 


8984 


8993 


9002 


9011 
9099 


9020 


9028 


9037 


9046 


9055 


9073 


9082 


9090 


491 


9108 


9117 


9126 


9135 


9144 


9152 


9161 


9170 


9179 


9188 


492 


9197 


9205 


9214 


9223 


9232 


9241 


9249 


9258 


9267 


9276 


493 


9285 


9294 


9302 


9S11 


9320 


9329 


9338 


9346 


9355 


9364 


494 


9373 


9381 


9390 


9399 


9408 


9417 


9425 


9434 


9443 


9452 


495 


9461 


9469 


9478 


9487 


9496 


9504 


9513 


9522 


9531 


9539 


496 


9548 


9557 


9566 


9574 


9583 


9592 


9601 


9609 


9618 


9627 


497 


9636 


9644 


9653 


9662 


9671 


9679 


9688 


9697 


9705 


9714 


498 


9723 


9732 


9740 


9749 


9758 


9767 


9775 


9784 


9793 


9801 


499 
500 


9810 


9819 


9827 
9914 


9836 


9845 


9854 


9862 


9871 


9880 


9888 


9897 


9906 


9923 


9932 


9940 


9949 


9968 


9966 


9975 


501 


9984 


9992 


70001 


70010 


70018 


70027 


70036 


70044 


70053 


70062 


502 


70070 


70079 0088 


0096 


0105 


0114 


0122 


0131 


0140 


0148 


503 


0157 


0165 0174 


0183 


0191 


0200 


0209 


0217 


0226 


0234 


504 


0243 


0252 


0260 


0269 


0278 


0286 


0295 


0303 


0312 


0321 


505 


0329 


0338 


0346 


0355 


0364 


0372 


0381 


0389 


0398 


0406 


506 


0415 


043,4 


0432 


0441 


0449 


0458 


0467 


0475 


0484 


0492 


507 


0501 


0509 


0518 


0526 


0535 


054^ 


0552 


056] 


0569 


0578 


508 


0586 


0595 


0603 


0612 


0621 


0629 


0638 


0646 


0655 


0663 


509 
510 


0672 


0680 


0689 


0697 


0706 


0714 


0723 
0808 


0731 


0740 


0749 


0757 


0766 


0774 


0783 


0791 


0800 


0817 


0825 


0834 


511 


0842 


0851 


0859 


0868 


0876 


0885 


0893 


0902 


0910 


0919 


512 


0927 


0935 


0944 


0952 


0961 


0969 


0978 


0986 


0995 


1003 


513 


1012 


102C 


1029 


1037 


1046 


1054 


1063 


1071 


1079 


1088 


514 


1096 


1105 


1113 


1122 


1130 


1139 


1147 


1155 


1164 


1172 


51.'i 


1181 


118£ 


1198 


1206 


1214 


1223 


1231 


1240 


1248 


1257 


51 f 


1265 


127J 


1282 


1290 


1299 


1307 


1315 


132^ 


1332 


1341 


51' 


1349 


135' 


1366 


1374 


1383 


1391 


1399 


1408 


1416 


1425 


51f 


1432 


144 


145C 


145& 


1466 


147a 


1483 


1492 


1500 


1509 


51J 


) 151' 


152. 


J 1533 


1542 


1550 


155S 


1567 


1575 


1584 


1592 





1 


1 2 


3 


4 


5 


6 


7 


8 


9 



A TABLE OF LOGARITHMS, 



IS 



' No. 5200—5800. 


Log. 71600—76^13, | 


NO.I 1 1 
' 520,71600,71609 


2 
71617 


3 


4 


5 1 6 


7 


8 
71667 


9 


716-25 


71634 


71642 


71630 


71659 


71675 


52r 1684 1692 


1700 


1709 


1717 


1725 


1734 


1742 


1730 


1759 


522i 1767 1775 


1784 


1792 


1800 


1809 


1817 


1826 


1834 


1842 


523 


1850 1858 


1867 


1875 


1883 


1892 


1900 


1908 


1917 


1925 


524 


1933 1941 


1950 


1958 


1966 


1975 


1983 


1991 


1999 


2008 


525 


2016! 2024 


2032 


2041 


2049 


2057 


2066 


2074 


2082 


2090 


526 


2099 


2107 


2115 


2123 


2 J 32 


2140 


2148 


2156 


2165 


2173 


527 


2181 


2189 


2198 


2206 


2214 


2222 


2230 


2239 


2247 


2265 


528 


2263 


2272 


2280 


2288 


2296 


2304 


2313 


2321 


2329 


2337 


529 
530 


2346 


2354 


2362 

2444 


2370 
2452 


2378 


2387 


2393 

2477 


2403 


2411 


2419 


2428 


2436 


2460 


2469 


2485 


2493 


2501 


531 


2509 


2518 


2526 


2534 


2542! 25501 2558 


2567 


2575 


2583 


532 


2591 


2599 


2607 


2616 


26241 2632] 2640 


2648 


2656 


2666 


533 


2673 


2681 


2689 


2697 


2705 


2713! 2722 


2730 


2738 


2746 


534 


2754 


2762 


2770 


2779 


2787 


2795' 2803! 2811 


2819 


2827 


535 


2835 


2843 


2852 


2860 


2868 


2876i 2884 


2892 


2900 


2908 
2989 


536 


2916 


2925 


2933 


2941 


2949 


2957 2965 


2973 


2981 


537 


2997 


3006 


3014 


3022 


3030 


3038 3046 


3054 


3062 


3070 


538 3078 


3086 


3094 


3102 


3111 


3119 3127 


3135 


3143 


3151 


539; 3159 
5401 3239 


3167 


3175 
^255 


3183 
3263 


3191 

3272 


3199 3207 


3215 


3223 


3231 


3247 


3280' 3288 


3296 


3304 


3312 


541 : 3320 


3328 


3336 


3344 


3352 


3360 3368 


3376 


3384 


3392 


5421 3400 


3408 


3416 


3424 


3432 


3440 


3448 


3456 


3464 


3472' 


543 34801 3488 


3496 


3504 


3512! 3520 


3528 


3536 


3544 


3552 
3632 


,544! 3560| 3568 


3576 


3584! 35921 3600 


3608 


3616 


3624 


545' 3640! 3648 


3666 


36641 36721 3679 


3687 


3695 


3703 


3711 


546] 3719 


3727 


3735 


3743 


3751 


3759 


3767 


3775 


3783 


3791 


547 3799 


3807 


3815 


3823 


3830 


3838 


3846 


3854 


3862 


3870 


5481 3878 


3886 


3894 


3902 


3910 


3918 


3926 


3933 


3541 


3949 


549; 3957 
550 4036 


3965 


3973 
4052 


3981 


3989 
4068 


3997 


4005 


40J3 
4092 


4020 


4028 


4044 


4060 


4076 


4084 


4099 


4107 


551 4115 


4123 


4131 


4139 


4147! 4155 


4762 


4170 


4178 


4186 


552 4194 


4202 


4210 


4218 


4225 


4233 


4241 


4249 


4257 


4266 


553 4273 


4280 


4288 


4296 


^304 


4312 


4320 


4327 


4335 


4343 


554 4351 


4359 


4367 


4374 


4382 


4390 


4398 


4406 


4414 


4421 


555, 4429 


4437 


4443 


4453 


446? 


4468 


4476 


4484 


4492 


4500 


556 4507 


4515 


452;J 


4531 


4J39 


4547 


4334 


4662 


4570 


4578 


557 4586 


4593 


4601 


46091 


4617 


4624 


4632 


4640 


4648 


4656 


558 4663 


4671 


4679 


4R57 


4695 


4702 


4710 


4718 


4726 


4733 


559 4741 

560 4819 


4749 


4757 
"5834 


4764 

4842 


4772 


4780 


4788 


4796 


4803 


4811 


4827 


4850 


4858 


4865 


4873 


4881 


4889 


561 1 4896 


490* 


4912 


4920 


4927 


4935 


4943 


4950 


4958 


4968 


562 4974 


4981 


4989 


4997 


5003 


6012 


3020 


6028 


6035 


5043 


563 5(^1 


5059 


5066 


5074 


3082 


5089 


5097 


5105 


5113 


5120 


564! ol28i 5136 


5143 


5151 


5159 


5166 


3174 


5182 


5189 


5197 


565! 52051 5213 


5220 


5228 


3236 


5243 


3251 


5259 


5266 


5274 


566 5282 5289 


5297 


5305 


5312 5320 


5328 


5335 


5343 


5351 


567' 5358! 5366 


5374 


5381 


5389 


3397 


5404 


3412 


5420 


3427 


568 1 5435 5442 


5450 


5458 


5465 


5473 


5481 


5488 


5496 


5504 


569; 5511 5519 
570 5587J 5595 


5526 
5603 


5534 


5542 


5549 


5357 


5565 


5572 


5580 


5610 


5618 


5626 


3633 


5641 


5648 


5656 


571 5664 


5671 


5679 


5686 5694 


6702 


5709 


5717 


5724 


5732 


572 5740 


5747 


5755 


5762 


5770 


3778 


5785 


5793 


6800 


5808 


573 5815 


5823 


5831 
5906 


3838 


3846 


6833 


6861 


5868 


5S76 


3884 


574 5891 


5899 


5914 


5921 


5929 


5937 


6944 


6952 


5959 


575 


5967 


5974 


5982 


5989 


5997 


6005 


6012 


6020 


6027 


6035 


576 


6042 6050 


6057 


6065 


6072 


6080 


6087 


6095 


6103 


6110 
6185 


577 


6118 6125 


6133 


6140 


6148 


6155 


6163 


6170 


6178 


578 


6193 6200 


6208 


6215 


6223 


6230 


6238 


6245 


6253 


6260 


.!>79 

KO. 


6268 6275 


6283 


6290 


6298 


6305 


6313 


6320 


6328 


6335 





1 1 


2 


3 


4 


5 


6 7 


8 


9 



14 



A TABLE OF LOGARITHMS. 





No. 6800— 6460. Log. '?(}it4JS— 80618. | 




HO. Oil 


2 


3 1 


4 


5 


6 


7 8 1 


9 




580 76543176350 


76358 763651 


76373 


76380 


76388 


76395 


76403 


7641C 




581 


6418 


6425 


6433 


64401 


6448 


6456 


6462 


6470 


6477 


6485 




582 


6492 


6500 


6507 


6516 


6522 


6630 


6637 


6545 


6562 


6569 




583 


6567 


6574 


6682 


6689 


6597 


6604 


6612 


6619 


6626 


6634 




584 


6641 


6649 


6666 


6664 


6671 


6678 


6686 


6693 


6701 


6708 




585 


6716 


6723 


6730 


6738 


6745 


6763 


6760 


6768 


6775 


6782 




586 


6790 


6797 6805 


68121 6819! 


6827 


6834 


6842 


6849 


6856 




587 


6864 


6871 6879 


6886 6893 


6901 


6908 


6916 


6923 


6930 




588 


6938 


6945, 6953 


6960 


6967 


6975 


6982 


6989 


6997 


7004 




589 
590 


7012 


7019 7026 
7093; 7100 


7034 


7041 


7048 

7122 


7066 


7063 


7070 


7078 




7085 


7107 


7116 


7129 


7137 


7144 


7161 




591 


7169 


7166' 7173 


7181 


7188 


7195 


7203 


7210 


7217 


7226 


592 


7232 


7240' 7247 


7264 


7262 


7269 


7276 


7283 


7291 


7298 




593 


7305 


7313 


7320 


7327 


7335 


7342 


7349 


7367 


7364 


7371 




594 


7379 


7386 


7393 


7401 


7408 


7416 


7422 


7430 


7437 


7444 




595 


7452 


7459 


7466 


7474 


7481 


7488 


7495 


7603 


7510 


7517 




696 


7525 


7532 


7539 


7546 


7554 


7561 


7668 


7676 


7583 


7690 




597 


7597 


7606 


7612 


7619 


7627 


7634 


7641 


7648 


7666 


7663 




598 


7670 


7677 


7685 


7692 


7699 


7706 


7714 


7721 


7728 


7735 




599 
600 


7743 


7760 


7767 


7764 


7772 


7779 


7786 


7793 


7801 
7873 


7808 




7815 


7822 


7830 


7837 


7844 


7851 


7869 


7866 


7880 




601 


7887 


7896 


7902 


7909 


7916 


7924 


7931 


7938 


7945 


7952 




602 


7960 


7967 


7974 


7981 


7988 


7996 


8003 


8010 


8017 


8026 




603 


8032 


8039 


8046 


8063 


8061 


8068 


8075 


8082 


8089 


8097 




604 


8104 


8111 


8118 


8125 


8132 


8140 


8147 


8164 


8161 


8168 




606 


8176 


8183 


8190 


8197 


8204 


8211 


8219 


8226 


8233 


8240 




606 


8247 


8264 


8262 


8269 


8276 


8283 


8290 


8297 


8305 


8312 




607 


S319 


8326 


8333 


8340 


8347 


8365 


8362 


8369 


8376 


8383 
8455 




608 


83SO 


8398 


8406 


8412 


8419 


8426 


8433 


8440 


8447 




B09 
610 


8462 


^69 
8540 


8476 

8647 


8483 
8554 


8490 


8497 


8504 


8512 


8619 


8526 




8533 


8561 


8569 


8676 


86a3 


8590 


8597 




611 


8604 


8611 


8618 


8625 


8633 


8640 


8647 


8654 


8661 


8868 




612 


8676 


8682 


8689 


H696 


8104 


8711 


8718 


8726 


8732 


8739 




613 


8746 


8753 


8760 


8'W 


8774'. «781 


8789 


8796 


8803 


8810 




614 


8817 


8824 


8831 


8838 


«845| 8852 


8869 


8866 


8873 


8880 




616 


8888 


8896 


8902 


8909 


8^16! 8923 


8930 


8937 


8944 


8951 




616 


8958 


8965 


8972 


8979 


89861 8993 


9(K)0 9007 


9014 


9021 
9092 




617 


9029 


9036 


9043 


9U6U 


9057 


1 "3064 


9071 


9078 


9086 




618 


9099 


9106 


9113 


9120 


9127 


1 91iH 


9141 


9148 


9155 


9162 




619 
620 


9169 


9176 


9183 


9190 


9197 


1 9204 


nil 

9281 


9218 


9225 9232 
9295 9302 




9239 


9246 


9263 


9260 


9267 


1 9274 


99,88 




621 


9309 


9316 


9323 


9330 


9337 


9344 


9351 


96&e 


9365 9372 




62? 


9379 


9386 


9393 


9400 


9407 


9414 


9421 


9428 


<1435 9442 




623 


9449 


9466 


9463 


9470 


9477 


9484 


9491 


9498 


95t« 9511 




m4 


9518 


9625 


9632 


9539 


954(] 


955a 


9560 


9567 


9574 


^581 




625 


9688 


9696 


9602 


9609 


96K 


962a 


963(J 


9637 


9644 


965rt 




69.6 


9657 


9664 


9671 


9678 


968£ 


9691ii 


969!J 


970b 


9715 


972C 




697 


9727 


9734 


974] 


9748 


9754! 9761 


976fc 


9775 


9785 


, 9789 




69,8 


9796 


9803 


9810 


9817 


9824! 9831 


983- 


9844 


9851 


9858 




629 

m 


9865 


9872 


9879 


9886 


9893: 990C 


990i 


99ia 


9921 


» 9927 




9934 


9941 


9948 


9955 


9962 996£ 


99U 


9982 


998S 


9996 




fiSl 


80003 


8001(1 


80017 


8002^ 


80030 8003'- 


80044 


80061 


8005t 


60065 




639 


(X)72 


0079 


008S 


0092 


0099 OlOC 


01 la 


0121 


012' 


0134 




63? 


014(1 


0147 


0164 


016; 


0168 017£ 


0182 


018i 


019f 


) 0202 




634 


0209 


0216 


022£ 


022S 


023f 


) 024S 


0251 


025- 


0264 


(.0271 




m 


0277 


0284 


0291 


0296 


(mt 


> 0312 


031!: 


082£ 


033i 


, 0339 




63( 


034^ 


03,5fl 


035f 


0366 


037i 


I 0381 


0381 


039a 


040( 


) 0407 




637 0414 


0421 


042f 


043^ 


044 


044? 


046£ 


0462 


046f 


0475 




638 0482 048£ 


049e 


0502 


050< 


) 05ie 


0523 


063C 


063e 


0543 




639 0550 0567| 056^ 


I 057C 


057' 


068^ 


069] 
6 


0596 


0604 


[ 0611 
9 




NO 


J- 0' 


1 1 


1 2 


3^ 


4 


6 


7 


6 



A TABLE OF LOGARITHMS. 



15 



-VT^m^r^m. 


Log. 8661 


§—34510. 1 


NO. 


1 


1 


2 


3 


4 5 


6 " 7 8 


9 


640 


80618,80625180632 


80638 


80645 80652 


80659 86665180672 80679 


641 


0686 


0693 


0699 


0766 


0713 0720 


0726 0733 0740, 0747 


642 


0754 


07601 0767 


0774 


0781 1 0787 


0794 0801 


0808; 0814] 


643 


0821 


0828 


0835 


0841 


0848 0855 


0862 0869 


0875 


0882 


644 


0889 


0895 


0902 


0909 


0916 0922 


0929 0936 


0943 


0949 


645 


0956 


0963 


0969 


0976 


0983 0990 


0996 1003 


1010 


1017 


646 


1023 


1030 


1037 


1043 


1050 1057 


1064 1070 


1077 


1084 


647 


1090 


1097 


1104 


1111 


1117 1124 


1131 1137 


1144 1151 


648 


1158 


1164 


1171 


1178 


1184 1191 
1551 1258 


1198 1204 


1211 1218 


649 


1224 


1^1 


'1238 


1245 


1266 1271 


1278 


1285 


650 


1291 


1298 


"1305 


1311 


1318; 1325 


1331 1 1338 


1345 


1351 


651 


1358 


1365 


1371 


1378 


1385 


1391 


1398 1405 


1411 


1418 


652 


1425 


1431 


1438 


1445 


1451 


1458 


1465 1471 


1478 


1485 


653 


1491 


1498 


1505 


1511 


1518 


1525 


1531 1538 


1544 


1551 


654 


1558 


1564 


1571 


1578 


15&i 


1591 


1598, 1604 


1611 


1617 


655 


1624 


1631 


1637 


1644 


1551 


1657 


1664i 1671 


1677 


1684 


656 


1690 


1697 


1704 


1710 


17171 1723 


1730, 1737 


1743 


1750 


657 


1757 


1763 


1770 


1776 


1783 


1790 


1796 1803 


1809 


1816 


658 


1823 


1829 


1836 


1842 


1849 


1856 


1862 1869 


1876 


1882 


659 
660 


1889 


1895 


1902 


1908 


1915 


1921 
"1987 


1928 1935 
1994 2000 


1941 


1948 


1954 


1961 


1968 


1974 


1981 


2007 


2014 


661 


2020 


2027 


2033 


2040 


2046 


2053 


2060 2066 


2073 


2079 


662 


2086 


2092 


2099 


2105 


2112 


2119 


2125 


2132 


2138 


2145 


663 


2151 


2158 


2164 


2171 


2178 


2184 


2191 


2197 


2204 


2210 


664 


2217 


2223 


2230 


2236 


2243 


2249 


2266 


2263 


2269 


2276 


665 


2282 


2289 


2295 


2302 


2308 


2315 


2321 


2328 


2334 


2341 


666 


2347 


23.54 


2360 


2367 


2373 


2380 


2387 


2393 


2400 


2406 


667 


2413 


2419 


2426 


2432 


2439 


2446 


2462 


2458 


2465 


2471 


668 


2478 


2484 


2491 


2497 


2504 


2510 


2617 


2523 


2530 


2536 


669 
670 


2543 


2549 


2556 
2620 


2562 


2569 


2676 


2682 


2688 
2653 


2595 


2601 


2607 


2614 


2627 


2633 


2640 


2646 


2659 


2666 


671 


2672 


2679 


2685 


2692 


2698 


2706 


2711 


2718 


2724 


2730 


672 


2737 


2743 


2750 


2766 


2763 


2769 


2776 


2782 


2789 


2795 


673 


2802 


2808 


2814 


2821 


28271 2834 


2840 


2847 


2863 


2860 


674 


2866 


2872 


2879 


2885 


2892 


2898 


2905 


2911 


2918 


2S24 


675 


2930 


2937 


2943 


2950 


2966 


2963 


2969 


2976 


2982 


2988 


576 


2995 


3001 


3008 


3014 


3020 


3027 


3033 


3040 


3046 


3052 


677 


3059 


3065 


3072 


3078 


3086 


3091 


3097 


3104 


3110 


311T 


678 


3123 


3129 


3136 


3142, 3149 


3155 


3161 


3168 3174 


318i 


679 

680 


3187 


3193 
3257 


3200 
3264 


3206: 32131 3219 
3270 3276; 3283 


3225 
3289 


3232 3238 
3296 3302 


3245 


3251 


3308 


681 


3315 


3321 


3327 


3334 3340i 3347 


3353 


3359 3366 


3372 


682 


3378 


3385 


3391 


3398-3404! 3410 


3417i 3423 


3429 


3436 


683 


3442 


3448 


3455 


3461 3467 3474 


3480] 3487 


3493 


3499 
3563 


684 


3506 


3612 


3518 


3525 3581 3537 


3544: 3650 


3656 


685i 3569 


3575 


3582 


3588 36941 3601 


3607 


3613 


3620 


3626 


686 


3632 


3639 


3645 


3651 3668 


3664 


3670 


3677 


3683 


3689 


687 


3696 


3702 


3708 


3715: 3721 


3727 


3734 


3740 


3746 


3753 


688 


3759 


3765 


3771 


3778i 3784 


3790 


3797 


3803' 3309 


3816 


689 
690 


3822 
3885 


3828 
3891 


3835 
3897 


3841 1 3847 
3904 3910 


3863 
3916 


3860 
3923 


3866| 3872 
3929! 3936 


3879 


3942 


691 


3948 


3954 


3960 


3967 3973 


3979 


3985 


3992 3998 


4001 


692 


4011 


4017 


4023 


4029; 4036 


4042 


4048 


4065 4061 


4067 
4130 


693 


4073 


4080 


4086 


4092 4098 


4105 


4111 


4117 4123 


694 


4136 


4142 


4148 


4155 4161 


4167 


4173 


4180 4186 


4192 


595 


4198 


4205 


4211 


4217 4223 


4230 


4236 


42421 4248 


4255 


696 


4261 


4267 


4273 


4280i 4286 


4292 


4298 


4305 


4311 


4317 


697 


4323 


4330 


4S36 


4342 4348 


4354 


4361 


4367 


4373 


4379 


698 


4386 


4392 


4398 


4404: 4410 


4417 


4423 


4429 


4435 


4442 


699 


4448 


4454 
1 


4460 


4466; 4473 


4479 
5 


4485 
6 


4491 

7 


4497 


4504 
9 





2 


3 


4 


8 



16 



A TABLE OF LOGARITHMS. 



No. 7000—7600." 




Log. 845 l(i— 88(1)8 l' 


NO.I 


1 


2 1 3 


4 1 5 


1 6- 1 7 : 8 i 9 












700 845 IC 


84516 


84522 84528 84535,84541 


84547, 8456384569 84566 


701 4572 


4578 


4584 4590 


4597 


4603 


4609 46151 462li 4628 


702 4634 


4640 


46461 4652 


4658 


4665 


4671 4677j 4685! 4689 


7031 4696 


4702 


4708 


4714 


4720 


4726 


4733 4739 4745 


4751 


704 


4757 


4763 


4770 


4776 


4782 


4788 


4794 4800 4807 


4813 


705 


4819 


4825 


4831 


4837 


4844 


4850 


4856' 4862 4868 


4874 


706 


4880 


4887 


4893 


4899 


4905 


4911 


4917 4924 4930 


4936 


707 


4942 


4948 


4954 


4960 


4967 


4973 


4979 4985 4991 


4997 


708 


5003 


5009 


5016 


6022 


5t)28 


6034 


5040 50461 6062 


5058 
6120 


709 
710 


5065 


5071 


5077 


5083 


6089 


5095 


5101 5107| 6114 


6126 


5132 


5138 


6144 


5150 


6156 


6163 


6169 .6175 


6181 


711 


5187 


6193 


5199 


5205 


5211 5217 


5224 


5230 5236 


6242 


712 


6248 


6254 


5260 


5266 


5272 6278 


5285 


52911 5297 


5303 


713 


5309 


5315 


5321 


6327 


5333 5339 


5345 


6352 


5368 


5364 


714 


5370 


5376 


5382 


5388 


5394 5400 


6406 


5412 


5418 


6425 


715 


5431 


5437 


5443 


5449 


5455, 6461 


5467 


6473 


6479 


5485 


716 


5491 


5497 


5603 


5509 


5516 


6622 


5528 


5534 


6540 


5546 


717 


5552 


5558 


5564 


.5570 


5576 


5582 


5588 


5594 


56001 6606 


718 


5612 


5618 


6626 


5631 


6637 


5643 


6649' 6655 


5661 5667 


719 

720 


5673 


5679 


6685 


5691 


5697 


6703 
6763 


5709 5715 
5769 3776 


57211 5727 


5733 


5739 


5745 


5751 


5757 


67811 6788 


721 


5794 


6800 


5808 


5812 


5818 


6824 


5830 6836 


6842 


6848 


722 


5854 


6860; 5866 


5872 


5878 


5884 


5890 6896 


6902 


5908 


723 


5914 


6920 


6926 


6932 


5938 


5944 


5950 5966 


6962 


6968 


724 


5974 


5980 


5986 


5992 


5998 


6004 


6010 6016 


6022 


6028 


725 


6034 


6040 


6046 


6052 


6058 


6064 


6070 6076 


6082 


6088 


726 


6094 


6100 


6106 


6112 


6118 


6124 


6130 6136 


6141 


6147 


727 


6153 


6159 


6165 


6171 


6177 


6183 


6189 6195 


6201 


6207 


728 


6213 


6219 


6225 


6231 


6237 


6243 


6249: 6256 


6261 


6267 


729 
730 


6273 


6279 


6285 


6291 


6297 


6303 


6308 
6368 


6314J 6320; 6326) 


6332 


6338 


6344 


6350 


6356 


6362 


6374 


6380' 6386 


731 


6392 


6398 


6404 


6410 


6415 


6421 


6427i 6433 


6439 6445 


732 


6451 


6457 


6463 


6469 


6476 


6481 


64871 6493 


6499] 6504 


733 6510 


6516 


6522 


6528 


6534 


6640 


6546i 6662 


6558! 6564 


734 


6570 


6576 


6581 


6587 


6593 


6599 


6605' 6611 


6617 6623 


735 


6629 


6635 


6641 6646 


6652 


6658 


6664 


6670 


6676 6682 


7Sfi 


6688 


6694 6700! 6705 


6711 


6717 


6723 


6729 


6735' 6741 


737 


6747 


6763 


6759 


6764 


6770 


6776 


6782 


6788 


6794| 6800 


7S8 


6806 


6812 


6817 


6823 


6829 


6836 


6841 


6847 


6853 6859 


739 

740 


6864 
6923 


6870 


6876 


6882 
6941 


6888 


6894 


6900 


6906 


6911J 6917 


6929 


6935 


6947 


6953 


6958 


6964 


6970 


6976 


741 


6982 


6988 


6994 


6999 


7005 


7011 


7017 


7023 


7029 


7035 


749. 


7040 


7046 


7052 


7058 


7064 


7070 


7076 


7081 


7087 


7093 


743 


7099 


7105 


7111 


7116 


7122 


7128 


7134 


7140 


7146 


7151 


744 


7157 


7163 


7169 


7176 


7181 


7186 


7192 


7198 


7204 


7210 


7i5 


7216 


7221 


7227 


7233 


7239 


7245 


7251 


7256 


7262 


7263 


746 


7274 


7280 


7286 


7291 


7297 


7303 


7309 


7315 


7320 


7326 


747 


7332 


7338! 7344 


7349 


7356 


7361 


7367 


7373 


7379 


7384 


748 


7390 


7396 


7402 


7408 


7413 


7419 


7425 


7431 


7437 


7442 


749 
750 


7448 


7454 


7460 


7466 


7471 


7477 


7483 


7489 
7547 


7496 


7500 


7506 


7512 


7518 


7523 


7629 


7636 


7641 


7552 


7658 


751 


7664 


7570 


7576 


7581 


7587 


7693 


7599 


7604 


7610 


7616 


752 


7622 


7628 


7633 


7639 


7646 


7651 


7656 


7662 


7668 


7674 


T53 


7679 


7685 


7691 


7697 


7703 


7708 


77141 7720 


7726 


7731 


754 7737 


7743 


7749 


7764 


7760 


7766 


7772 ,7777 


7783 


7789 


755 7795 


7800 


7806 


7812 


7818 


7823 


7829 7836 


7841 


7846 


756 7852 


7858 


7864 


7869 


7876 


7881 


7887 7892 


7898 


7904 


767 7910 


7915 


7921 


7927 


7933 


7938 


7944 7950 


7965 


7961 


758 7967 


7973 


7978 


7934 


7990 


7996 


8001 8007 


8013 


801.8 


769 


8024 


8030 


8036 


8041 


8047 


8053 


8058 8064 


8070 


8076 
9 


ko. 





1 [ 2 


3 


4 


5 


6 7 


8 



A TABLE OP LOGARITHMS. 



17 



N 


0. 7600—8200. 








Log 


88081—91381. 1 


NO. 





1 


2 , 


3 1 


4 


5 1 


6 


7 1 


8 1 


9 


76088081 


88087 88093 


38098 88104 88110 88160' 


88121i88127!88133l 


761 


8138 


8144 


8150 


8156 


8161 


8167 


8173 


81781 


8184 


8190 


762 


8196 


8201 


8207 


8213 


8218 


8224 


82301 


8235: 


8241 


8247 


763 


8252 


8253 


8264 


8270 


8275 


8281 


8287, 


8292 


8298 


8304 


764 


8309 


8315 


8321 


8326 


8332 


8338 


8343 


8349 


8355 


8360 


765 


8366 


8372 


8377: 


8383 


8389 


8395 


8400 


8406 


8412 


8417 


766 


8423 


8429 


8434, 


8440 


8446 


8451 


8457 


8463 


8468 


8474 


767 


8480 


8485 


8491 


8497 


8502 


8508 


8513 


8519 


8525 


8530 


768 


8536 


8542 


8547 


8553 


8559 


8564 


8570 


8576 


85811 8587! 


769 
770 


8593 
8649 


8598 
8655 


8604 
8660 


8610 
8666 


8615 
8672 


8621 
8677 


862> 
8683 


8632 
8689 


8638 
8694 


8643 


8700 
8756 


771 


8705 


8711 


8717 


8722 


8728 


8734 


8739 


8745 


8750 


772 


8762 


8767 


8773 


8779 


8784 


8790 


8795 


8801 


8807 


8812 


773 


8818 


8824 


8829 


8835 


8840 


8843 


8852 


8857 


8863 


8868 


774 


8874 


8880 


8885- 


8891 


8897 


8902 


8903 


8913 


8919 


8925 


775 


8930 


8936 


8941 


8947 


8953 


8958 


8964 


8969 


8975 


8981 


776 


8986 


8992 


8997 


9003 


9009 


9014 


9O20 


9025 


9031 


9037 


777 


9042 


9048 


9053 


9059 


9064 


9070 


9076 


081 


087 


092 


778 


9098 


9104 


9109 


9115 


9120 


9126 


9131 


137 


143 


148 


779 


9154 


9159 


9165 


9170 


9176 


9182 


9187 


193 


193 


iOi 






















260 
315 


780 


9209 


9215; 


9221 


S226 


9232 


9237 


9243 


248 


254 


781 


9265 


9271 


927S 


9282 


9287 


9293 


9298 


304 


310 


782 


9321 


9326 


9332 


9337 


9343 


9348 


9354 


360 


365 


371 


783 


9376 


9382 


9387 


9393 


9398 


9404 


9409 


415 


421 


426 


784 


9432 


9437 


9443 


9448 


9454 


9459 


9465 


470 


476 


481 


785 


9487 


9492 


9498 


9504 


9509 


9515 


9520 


626 


531 


537 


786 


9542 


9548 


9553 


9559 


9564 


9570 


9575 


581 


586 


592 


787 


9597 


9603 


9609 


9614 


9620 


9625 


9631 


636 


642 


647 


788 


9653 


9658 


9664 


9669 


9675 


9680 


9636 


691 


697 


702 


789 


9708 


9713 


9719 


9724 


9730 


9735 


9741 


746 


752 


757 


790 


9763 


'97681 


9774 


9779 


9785 


9790 


9796 


801 


807 


812 


791 


9818 


9823 


9829 


9834 


9840 


9845 


9851 


856 


862 


867 
922 


792 


9873 


9878 


9883 


9889 


9894 


9900 


9905 


911 


916 


793 


9927 


99331 


9938 


9944 


9949 


9955 


9960 


966 


971 


977 


794 


9982 


9988' 


9993 


9998 90004 90009 90015 


90020 


90026 


90031 


795 


90037 


90042 '90048 90053 


0059 


0064 


0069 


0075 


0080 


0086 


796 


0091 


0097 


0102 


0108 


0113 


0119 


0124 


0129 


0135 


0140 


797 


0146 


0151 


0157 


0162 


0168 


0173 


0179 


0184 


0189 


0195 


798 


0200 


0206 


0211 


0217 


0222 


0227 


0233 


0238 


0244 


0249 
0304 


799 


0255 


0260 


0266 


0271 


0276 


0282 


0287 


0293 


0298 


800 


0309 


0314 


0320 


0325 


0331 


0336 


0342 


0347 


0352 


0358 


801 


0363 


0369 


0374 


0380 


0385 


0390 


0396 


0401 


0407 


C412 


802 


0417 


0423 


0128 


0434 


0439 


0445 


0450 


0455 


0461 


0466 


803 


0472 


0477 


0482 


0488 


0493 


0499 


05(J4 


0509 


0515 


0520 


804 


0526 


0531 


0536 


0542 


0547 


0553 


0558 


0563 


0569 


0574 


805 


0580 


0585 


0590 


0596 


0601 


0607 


0612 


0617 


0623 


0828 


606 


0634 


0639 


0644 


0650 


0655 


0660 


0606 


0671 


0677 


0682 


807 


0687 


0693 


0698 


0703 


0709 


0714 


0720 


0725 


0730 


0736 


808 


0741 


0747 


0752 


0757 


0763 


0768 


0773 


0779 


0784 


0789 
0843 


809 


0795 


0800 


0806 


0811 


0816 


0822 


0827 


0832 


0838 


810 


0849 


0854 


0859 


0865 


0870 


0875 


0881 


0886 


0891 


0897 


811 


0902 


0907 


0913 


0918 


0924 


0929 


0934 


0940 


0945 


0950 


312 


0956 


0961 


0966 


0972 


0977 


0982 


0988 


0993 


0998 


1004 


813 


1009 


1014 


1020 


1025 


1030 


1036 


1041 


1046 


1052 


1057 


814 


1062 


1068 


1073 


1078 


1084 


1089 


1094 


1100 


1105 


1110 


815 


1116 


1121 


1126 


1132 


1137 


1142 


1148 


1153 


1158 


1164 


816 


1169 


1174 


1180 


1185 


1190 


1196 


1201 


1206 


1212 


1217 
1270 


817 


1222 


1228 


1233 


1238 


1243 


1249 


1254 


1259 


1265 


818 


1275 


1281 


1286 


1291 


1297 


1302 


1307 


1312 


1318 


1323 


819 


132« 


1334 


1339 


1344 


1350 


1355 


1360 


1365 


1371 


1376 


NO. 





i 1 


2 


3 


4 


5 i 


6 


' 


8 


9 



16 



A TABLE OF LOGARITHMS. 



No. "8200—8800. 


Log. 91381— 94448. f 


NO.I 1,2 


3 


4 


5 


6 , 7 


8 


9 


820,9138191387,91392 


91397 


91403 


91408 


9141391418 


91424 


91429 


821 


1434 1440 


1445 


1450 


1455 


1461 


1466! 1471 


1477 


1482 


822 


1487 1492 


14S8 


1503 


1508 


1514 


1519! 1524 


1529 


1535 


823 


1540 1545 


1661 


1556 


1661 


1566 


1672: 1577 


1582 


1587 


824 


1593 


1598 


1603 


1609 


1614 


1619 


1624t 1639| 1635 


1640 


825 


1645 


1651 


1656 


1661 


1666 


1672 


1677' 16821 1687 16931 


826 


1691 


1703 


1709 


1714 


1719 


1724 


1730i 17351 1740 17451 


827 


1751 


1756 


1761 


1766 


1772 


1777 


1782 


17871 1793 17981 


828 


1803 


1808! 1814 


1819 


1824 


1829 


1834 


1840! 1845! 1850| 


829 
830 


1855 


1861 


1866 
1918 


1871 


1876 


1882 


1887 


1892 


1897! '^O^j 


1908 


1913 


19241 1929 


1934 


1939 


1944 


1950 19651 


831 


1960 


1965 


1971 


19761 1981! 1986 


1991 


19971 2002j 2007 


832 


2012 


2018 


2023 


2028 2033! 2038 


2044 


2049 2064: 2069 


833 


2065 


2070 


2076 


2080 2086! 2091 


2096 


2101 2106! 2111 


834 


2117 


2122 


2127 


2132 2137 


2143 


2148 


2153 2158i 2163 


835 


2169 


2174 


2179 


21841 2189 


2195 


2200 


2203» :i21D! 2215 


836 


2221 


2226 


2231 


2236 2241 


2247 


2252 2267^ 2262| 2267 


837 


2273 


2278 


2283 


2288' 2293 


2298 


2304 23091 2314! 2319 


838 


2324 


2330 


2335 


2340 2345 


2350 


2356 2361, 2366 2371 


839 
840 


2376 


2381 


2387 


2392 2397 
2443 2449 


2402 
2454 


2407 2412 
2459 2464 


2418: 24231 


2428 


2433 


2488 


2469 2474 


841 


2480 


2485 


2490 


2496 2500 


2605 


2511 2516 2521' 2526 


842 


2531 


2536 


2542 


2547 2552 


2557 


2662 2667 2672 2578 


843 


2583 


2588 


2593 


2698 2603 


2609 


2614 2619 2624 2629 


844 


2634 


2639 


2645 


2650 2655 


2660 


2665 2670 2675 2681 


845 


2686 


2691 


2696 


2701 2706 


2711 


2716 2722 2727 2732 


846 


2737 


2742 


2747 


2752 2758 


2763 


2768 2773 2778 2783 


847 
848 


2788 


2793 


2799 


2804 2809 


2814 


2819 2824 2829 2834 


2840 


2845 


2850 


2856 2860 


2865 


2870 2875 2881 2886 


849 
850 


2891 


2896 


2901 


2906 2911 


2916 


2921 2927 2932 


29371 


2942 


2947 


2952 


2957 2962 


2967 


2973 2978 2983 


2988! 


851 


2993 


2998 


3003 


3008 3013 


3018 


3024 3029 3034: 3039 


852 


3044 


3049 


3054 


3059 3064 


3069 


3075 3080 3085 3090 


853 


3095 


3100 


3106 


3110 3115 


3120 


3125 3131 3136 3141 


854 


3146 


3151 


3156 


3161 3166 


3171 


3176 3181 1 3186 3192 


855 


3197 


3202 


3207 


3212 3217 


3222 


3227 3232: 3237 3242 


856 


3247 


3252 


3258 


3263 3268 


3273 


3278 3283! 3288 3293 


857 


3298 


3303 


3308 


3313 3318 


3323 


3328 3334! 3339 3344 


858 


3349 


3354 


3359 


3364 3369 


3374 


3379 3384j 3389 3394 


859 
860 


3399 


3404 
3455 


3409 


3414 3420 
3465 3470 


3425 


3430 3435 1 3440 3445 


3450 


3460 


3475 


3480 34851 3490 3495 


861 


3500 3505 


3510 


3515 3520 


3526 


3631 3536! 3541 3546 


862 
863 


3551 3556 


3661 


3566 3571 


3576 


368L 3586: 3591 3596 


3601 3606 


3611 


3616 3621 


3626 


3631 3636! 3641 3646 


864 


36511 3656 


3661 


3666 367 r 3676 


3682 3687' 3692 3697 


865 


3702; 3707 


3712 


3717 3722 


3727 


3732 3737 3742 3747 


866 


37521 3767 


3762 


3767 3772 


3777 


3782 3787i 3792 3797 


867 


3802, 3807 


3812 


3817 3822 


3827 


3832 3837! 3842 3847 


868 3852 3857 3862| 


3867 3872; 3877 


3882 3887; 3892 3897 


869 3902 


3907 3912 


3917 3922 3927 


3932 3937; 3942 3947 


870 3952 


3957 3962 


3967 3972; 3977 


3982 3987 


3992 3997 


871, 4002 


4007 4012 


4017 4022: 4027 


4032 4037 


4042: 4047 


872i 4052 


4057 4062 


4067 4072 


4077 


4082 4086 


4091! 4096 


873; 4101 


4106 4111 


4116 4121 


4126 


4131 4136 


41411 4146 


874 


4151 


4166 4161 


4166 417a 


4176 


4181 4186 


4191 


4196 


875 


42011 4206 4211 


4216, 4221 


4226 


4231 4236 


4240 


4246 


876 


4250| 4255 4260 


4265! 4270 


4275 


4280 4286 


4290 


4296 


877 
878 


4300i 4305' 431(1 


43151 4320 


4325 


4330^ 4335 


4340 


4345 


4349i 4354 


4359 


4364! 4369 


4374 


4379! 4384 


4389 4394 
4438 4443 


879 


4399' 4404 


4409 


4414! 4419 


4424 


4429 4433 


NO. 


1 


2 


3 1 4 


^5_ 


6 1 7 


8 9 



A TABLE OP LOGARITHMS. 



1^ 



TRSTssiKv-glwJ: 




Log 


. 94448—97313. | 


NO. 1 j 2 1 3 


4 


5 16. 


7" 


8 1 9 


880 94448 g4453'94458'94463 


94468 


94473!9447894483 


94488,94493 


881 


4498 


4503' 4507' 4512 


4517 


4522 


4527 


4532 


45371 4542 


882 


4547 


4552; 4557; 4562 


4567 


4571 


4576 


4581 


4586; 4591 


883 


4596 


4601 


4606 


4611 


4616 


4621 


4626 


4630 


4635J 4640 


884 


4645 


4650 


4655 


4660 


4665 


4670 


4675 


4680 


46851 4689 


885 


4694 


4699 


4704 


4709 


4714 


4719 4724 


4729 


4734 4738 


886 


4743 


4748 


4763 


4758 


4763 


4768 4773 


4778 


4783 4787 


887 


4792 


4797 


4802 


4807 


4812 


4817, 4822 


4827 


4832 4836 


888 


4841 


4846 


4851 


4856 


4861 


4866 4871 


4876 


4880: 4885 


889 
890 


4890 


4895 


4900 
4949 


4905 


4910 


4915 4919 
4963 4968 


4924 
4973 


4929. 4934 


4939 


4944 


4954 


4959 


49781 4983 


891 


4988 


4993 


4998 


5002 


5007 


5012 6017 


5022 


50271 5032 


892 


5036 


5041 


5046 


5051 


5056 


50611 5066 


5071 


5075; 5080 


893 


5085 


5090 


5095 


5100 


5105 


5109 5114 


5119' 51241 5129 


894 


5134 


5139 


5143 


5148 


5153 


5158 5163 


51681 5173, 5177 


895 


5182 


5187 5192 


5197 


5202 


5207 5211 


5216 5221 5226 


896 


5231 


5236| 5240 


5246 


5250 


5255 5260 


5265 5270 5274 


897 


5279 


6284! 5289 


5294 


5299 


6303 5308 


5313 5318 5323 


898 


5328 


5332 5537 


5342 


5347 


5352 5357 


6361 5366 5371 


899 


6376 


5381 6386 


5390 


5395 


5400 5405 


5410 5416 5419 


900 


5424 


5429 5434 


5439 


5444 


5448 5453 


5458 1 5463 5468 


901 


5472 


5477: 5482 


5487 


5492 


5497 5501 


5506 6511 5516 


902 


5521 


5525' 5530 


5535 


5540 


5545 5650 


5554: 5559 5564 


903 


5569 


5574: 5578| 5583 


5588 


5693 5698 


6602 5607 5612 


904 


5617 


56221 56261 5631 


5636 


5641 5646 


6660 5655 5660 


905 


5665 


5670 56741 5679 


5684 


5689 5694 


5698 5703 5708 


906 


5713 


5718! 57221 5727 


5732 


5737 5742 


6746 5751 5756 


907 


5761 


5766i 5770 5775 


5780 


5785 5789 


5794 5799 5804 


908 


5809: 5813 6818i 5823 


5828 


5832 5837 


5842 5847 5852 


909 


5856 5861 5866; 5871 


5875 


6880 5885 


5890 5895 5899 


910 


5904; 5909 5914i 5918 


5323, 


5928 5933 


5938 5942 5947 


911 


5952| 5957 5961! 5966 


5971 


5976 5980 


5985 5990 5995 


912 


5999i 6004; 6009| 6014, 


6019 


6023 6028 


6033 6038 6042 


913 


6047' 6052 6057| 6061' 


6066 


6071 6076 


6080 6085 6090 


914 


6095 6099 


6104! 6109 


6114 


6118 6123 


6128 6133 6137 


916 


6142 6147 


61521 6156 


6161 


6166 6171 


6175 6180 6185 


916 


6190 6194 


6199 6204 


6209 


6213 6218 


6223 6227 6232 


917 


6237 6242 6246; 6251 


6266 


6261 6265 


6270 6275 6280 


918 6284 6289 62941 6298 


6303 


6308 6313 


6317 6322 6327 


919 6332 6336 6341 6346 


6350. 


6356 6360 


6365 6369 6374 


920 6379 6384 63881 6393 


6398, 


6402 6407 


6412 6417 6-121 


921' 6426 6431 6435 6440 


6445 


6450 6454 


6459 6464 6468 


922 6473 6478 6483 6487 


6492 


6497 6501 


6506 6511 6515 


923 6520 6525 6530 6534 


6539 


6644 6548 


6553 6558 6562 


924 6567 6572 6577 6581 


6586 


6691 6596 


6600 6605 6609 


925' 6614 6619 6624 6628 


6633 


6638 6642 


6647 6652 6656 


926 6661 6666 6670 6675 


6680 


6685 6689 


6694 6699 6703 


927 6708 6713 6717 6722 


6727 


6731 6736 


6741 6745 6750 


928 6755 6759 6764 6769 


6774 


6778 6783 


6788 6792 6797 


929; 6802 6806 6811 6816 


6820 


6825 6830 


6834 6839 6844 


930 6848 6853 6858 6862 


6867 


6872 6876 


6881 6886 6890 


931 6895 6900 6904 6909 


6914 


6918 6923 


6928 6932 6937 


932 6942 6946 6951 6956 


6960 


6965, 6970 


6974 6979 6984 


933 6988 6993 6997 7002 


7007 


70111 7016 


7021 7025 7030 


934 7035 7039 7044 7049 


7053 


70681 7063 


7067 7072 7077 


935 7081 7086 7090 7095^ 


7100 


71041 7109 


7114 7118 7123 


936 7128 7132 7137 7142 


7146 


71511 7155 


7160 7165 7169 


937 7174 7179 7183 7188 


7192 


7197 7202 


7206 7211 7216 


938 7220 7225 7230 7234 


7239 


7243 [ 7248 


7253, 7267 7262 


939 7267 7271 7276 7280 


7285. 


7290. 7294 


7299, 7304, 7308 


No.l 1 1 1 2 .| 3 1 


4 1 


5 1 6_^ 


7 19 19 



ZQ 



A TABLE OP LOGARITHMS. 



"Nd."9400~l(X)00. 



Log. 97313—9 9996. 



NO., . 1 i 2 I 3 , 4 5_|_^,_2 L_l^_ 

940 97313 97317 97322 97327 97331 97336 97340 97345 97350 97354 

941 7359i 7364; 7368! 7373i 7377 7382 7387 7391 7396 7400 

942 7405^ 7410' 7414' 7419 7424 7428 7433 7437 7442 7447 

943 7451' 74561 7460! 7465: 7470 7474 ■ 7479 7483 74881 7493 

944 7497' 7502' 7606! 7511 7516 7520 7525 7529 7534} 7539 

945 7643 7548' 7552: 7567' 7562 7566 7571 7575 7580 7585 

946 7589 7594 7598 7603 7607 7612 7617 7621 7626 7630 

947 7635 7640 7644 7649 7653 7658 7663 7667 7672 7676 

948 7681 7685 7690 7695 7699 7704 7708 7713 7717} 7722 

949 7727 7731 7736: 7740; 7745 7749 7754 7759 7763] 776j 
950 'iTTO'rm 1782 ~7786i 7791 ~7795 7800 7804 78091 7813 
951 7818 7823 7827' 7832 7836 7841 7845 7850 7855: 7859 
962 7864 7868 7873 7877: 7882 7886 7891 7896 7900i 7905 

953 7909: 7914 7918 7923' 7928 7932 7937 7941 79461 7950 

954 79561 7950 7964 7968! 7973 7978 7982 7987 7991! 7996 

955 8000| 8005 8009 8014; 8019 8023 «Q28 8032 8037! 8041 

956 8046' 8050 8055 8069 8064 8068 8073 8078 8082J 8087 

957 80911 8096 8100 8105' 8109 8114 811^ 8123 8127 8132 

958 8137 8141 8146 8150 8155 8159 8164 8168 81731 8177 

959 8182! 8186 8191, 8195 8200 8204 8209 8214 8218 ; 822 3 
980 6227! "8232 "8236''8241!'"8245 "8250 8254 8259 8263 "8268 

961 8272! 8277 8281 8286! 8290 8295 8299 8304 8308; 8313 

962 8318i 8322 8327 8331 ! 8336 8340 8345 8349 8354] 8358 

963 8363; 8367 8372 8376' 8381 8385 8390 8394 8399! 8403 

964 8408; 8412 8417 8421' 8426 8430 8435 8439 8444: 8448 

965 8453 8457 8462 8466' 8471 8475 8480 8484 8489' 8493 

966 8498 8502 8507 8511; 8516 8520^ 8525 8529 8534; 8538 

967 8543 8647 8552 85561 8661 8666 8570 8574! 8579] 8583 

968 8588 8592 8597 86011 8605 8610 8614 8619 8623i 8628 

969 - 8632 8637 8641 ■ 8646; 8650 8655 865 9 8664 8668 ! 8673 

970 8677 "8682 "8686 8691! 8695 8700 8704 8709 8713! 8717 

971 8722 8726 8731 8735: 8740 8744 8749 8753: 8758! 8762 
972' 8767 8771 8776 8780 8784 8789 8793 8798' 88021 8807 

973 8811 8816 8820 8826) 8829 8834 8838 8843: 8847| 8851 

974 8866; 8860 8866 8869 8874 8878 8883 8887, 8892; 8896 
8905; 8909 89141 8918 8923 8927 8932; 89361 8941 
8949 8954 8958| 8963 8967 8972 8976i 8981! 8985 
8994 8998 90031 9007 9012 9016 9021' 9026 9029 

047j 052 056 061 065i 0691 074 
092' 096 100| 105 

149 

193 

238 



976 8900 

976 8946 

977 8989 
978; 9034 
979: 9078 




Jlrtificial Sines, Tangents, and Secants. 2 1 



Mi Sine , C. Sine 



Degree. 



0.0000010.00000 

5 7.16270] 00 

10 46373 00 

15, 63982' 00 

20' 76475, 9.99999 

25, 86166i 99 

30 940841 98 



35 8.00779 9.99998 



0657S 
11693 
16-268 
20407 
24186 



C. Sine! Sine 



Tang. ,C.Tang, 



Secant. iC. Sec.i M 



O.OOOOOI Infinite 
7. 16270! 12. 83730 



46373 
63982 
76476 
86167. 
94086! 



53627 
36018 
23524 
13833 
05914 



10,000001 Infinitel 60 
00 12.83730; 65 
00 53627, 50 



8.0078111.99219 



06581 i 
1169S| 
16273 
20413 
241921 



93419 
88304 
83727 
79587 
75808 



C.Tan?.! Tana 



36018' 45 
23525' 40 
13834' 35 
05915 30 



10.0000211.99221 25 



03 
04 
05 
06 

07 

C. Sec. 



93422 20 
88307 i 15 
83732 10 
79593! 6 
75814 



Secant M 



89 Degrees. 



1 Degree. 



M Sine i C. Sine; Tan?. C.Tang.i Secant. C. Sec. M 



8.241861 9.99993i 8,2419211.75808 



27661 
30879 
33875 
36678 
39310 
41792 



92! 276691 

91 i 30888! 

89 33886 j 

88 366891 

87 1 39323 

85 41807 



72331 
69112 
66114 
63311 
60677 
58193 



10.00007 
08 
09 
11 
12 
13 
15 



11.75814: 60 
72339' 55 
69121! 50 
66125 45 
63322 40 
60690' 35 
58208 30 



8.44139, 

4636& 

48485 
50505 

52434 
54282 



9.99983 8.44156 11.55844 ia00017ill. 558611 25 

82' 46385 536151 18| 53634 20 

80 48505 51495 20! 51515 15 

78 50527 49473 22' 49495 10 

76' 52459 47541 24! 47566 5 

74 54308 45692 26i 45718 



C. Sine' Sine 



C .Tang. I Tang. | C. Sec! Secant.! M 



88 Degrees. 
2 Degrees. 



Ml Sine 



C. Sine; Tang. C.Tang.| Secant , C. Sec. | M 
9.99974 8.54308 11.45692* 10.00026|ll.45718!"60 




22 Artificial Sines, Tangents, and Secants. 



3 Degrees. .| 


M 


Sine 


C. Sine 


Tang. C.Tang. Secant 
8.71940 1 1.28060, 10.0006C 


C. Seel M] 


C 


8.7188C 


9.99940 


11.28120 


60 


5 


7306S 


37 


73132, 2686{ 


63, 26931 


55 


1( 


74226 


3^ 


74292, 25708 


66 25774 


60 


IS 


75353 


30 


75423 24577 


70 24647 


45 


2( 


7645] 


26 


76525: 23475 


74 2354E 


40 


25 


77522 


2i 


77600: 2240( 


77. 22478 


35 


30 


78567 


19 


78649; 21351 
8.79673 11.20327 


81 
10.-0008S 


! 21433 


30 


35 


8.79588 9.99915 


11.20412 


25 


40 


80585. 11 


80674 19326 


89 19415 


20 


45 


81560, 07 


816531 18347 


93 18440 


15 


50 


82513' 03 


82610! 1739C 


97 17487 


10 


55 


83446 98898 


83547' 16452 


102! 16554 


5 


60 


84358 


894 


84464 15536 


106 


! 15642 
1 Secant 




Ivi 


Ml G. Sine 


Sine 


C.Tang.' Tang. IC. Sec. 


86 Degrees. 


4 Degrees. 


M 


Sine 


C. Sine 


Tang. 


C.Tang. 


Secant 


C. Sec. 


fll 





8.84358 


9.99894 


8.84464 


11.16536 


10.00106 


11.15642 


60 


5 


85252 


890 


8536E 


14637 


110 


14748 


65' 


10 


86128 


885 


8624£ 


13757 


115 


13872 


50 


15 


86987 


880 


87106 


12894 


120 


13013 


45 


20 


87829 


876 


87953 


12047 


124 


12171 


40 


25 


88654 


671 


88783 


11217 


129 


11346 


3,7 


30 


89464 


866 


89598 
8.90399 


10402 


134 


10536 


30 

25 


35 


8.90260 


9.89861 


11.09601 


10.00139 


11.09740 


40 


91040 


856 


91185 


08815 


144 


08960 


20 


45 


91807 


851 


91957 


08043 


149 


C8193 


15 


50 


92561 


845 


92716 


07284 


155 


07439 


"1 


55 


93302 


840 


93462 


06538 


160 


06698 


5 


60 94030 


834 
Sine 


94195 


05805 


166 05970 
C. Sec. Secant 





M! C. Sine 


C.TangJ: Tang. 


85 Degrees. | 




Degrees. g 


ftl 


Sine 1 C. Sine' 


Tang, j C.Tang. Secant jC. Sec W 


Oj 8.94030 


9.99834 


8.94195 11.05805,10.00166 11.05970, 6Q 


5 94746 


829 


94917 


05083 


171 


05254 55 


10 95450 


823 


95627 


04373 


177 


04550 50 


15 


961431 817 


96325 


03675 


183 


03857 


45 


20 


968251 812 


97013 


02987 


188 


03175 


40 


25 


97496 806' 97691 


02309 


194 


02504 


35 


30 


98157 


800 98358 


01642 


200 


01843 


30 
25 


35 


8.98808 


9.99794 1 8.99015 


11.00985 


10.00206 


11.01192 


40 


99450 


787 


99662 


00338 


213 


00560 


20 


45 


9.00082 


781 


9.00301 


10.99699 


219 


10.99918 


15 


60 


.. 00704 


775 


00930 


99070 


225 


99296 


10 


65 01318 


768 


01550 


98450 


232 


98682 


5 


60 01923 


761 


02162 


97838 


239 


98077 




M 


"Ml C. Sine 


Sine 


C.Taiig. 


Tang. 


C. Sec. 


Secant 


84 Degrees. 1 



Artificial Sines, Tangents, and Secants. 23 



6Degrees. 



Mj Sine C. Sine Tang. C.Tang. Secant | C. Sec. M 



9.01924 9.99761 9.0216210.9783810.0023910.98076 60 



02520 
03109 
03690 

04263 
04828 
05386 



755 

7481 

741! 

'734! 

727 1 
720: 



02765 

03361 

03949 

04528- 

05101 

05666 



97235 
96639 
96051 
95472 



94334 



245 
352 
259 
2661 
273 
280, 



97480 55 
96891 50 
96310 45 
95737 40 
95172 35 
94614; 30 



9.05937 
06481 
07018 
07548 
08072 
08589 



9.99713 9.06224 10.93776 10.00287 10.94063| 25 



705 i 
698i 
6901 
683: 
675: 



06775 
07320 
07858 
08389 
08914 



93225 295 

92680 302 

92142 310 

91611 3171 

91086 325i 



935191 20 

92982! 15 
92452 
91928 
91411 



C. Sine Sine C.Tana;. Tan?. C. Sec. Secant M 



83 Degrees. 
7 Degrees. 



M 

"0 
5 
10 
15, 

2o: 

25 
30 



Sine I C. Sine; Tang. jC.Tang. Secant C. Seel M 



9.08589| 
091011 
096061 
10106 
10599 
11087 
11670 



10.00325 10.91411 60 
333, 90899, 55 



9.99675 9.0891410.91086 

667| 09434 90566 

669 1 09947 900531 341 ' 90394; 50 

661 10454 89546] 349| 89894 45 

643 10956 89044, 357; 89401: 40 

635 11452 885481 3651 88913i 35 

627 11943! 880571 373 88430 30 



t;. 120471 
12619 
129851 
13447! 
13904! 
143561 



9.99618i 9.12428:10.87572 

610! 12909' 87091 

602! 133841 86616 

6^1 13864! 86146 

5841 14320! 85680 

575' 14780! 86220 



10.00382 10.87963 25 
390, 87481! 20 



398: 
4071 
416: 
4251 



87015! 15 

86563' 10 

86098: 5 

85644' 



M C.Sine Sine C.Tang.' Tang. iC. Sec' Secant i M 



82 Degrees. 



8 Degrees. 



M Sine | C. Sine| Tang. , C.Tang. | Secant |C. Sec.! JM 
9.995761 "9. 14780 10.86220, 1000425 ,1085644 ! ~60 



9.14356 
14803! 
15245 
15683; 
16116: 
16545 
16970 



566 
557 
548 
539 
530 
520i 



9.17391 
178071 
182201 
18628| 
19033 
194331 



15236 


84764 


434 


15688 


84312 


443 


16135 


83865 


452 


16677 


83423 


461 


17016 


82984 


470 


17450 


82560 


480 



85197! 55 
84765! 50 
843171 45 
838841 40 
83455 35 
83030 30 



9.99611 9.1788010.82120 10.00489 10.82609 25 



501 

492 
482 
472 
462 



M C. Sine 



18306 


81694 


499 


82193 


18728 


81272 


508 


81780 


19146 


80854 


518 


81372 


19561 


80439 


528 


80967 


19971 


80029 


538 
C. Sec. 


80567 
Secant 


C.Tang. 


Tang. 



81 Degrees. 



^4 Artificial Sines, Tangents, and Secants. 





9 Degrees. | 


M 




Sine 


C. Sine 


Tang. 


C.Tang. 
10.80029 


Secant 


C. Sec. 


M 

60 


9.19433 


9.99462 


9.19971 


10.00538 


10.80567 


5 


19830 


452 


20378 


79622 


548 


80170 


55 


10 


20223 


442 


20782 


79218 


558 


79777 


50 


15 


20613 


432 


21182 


78818 


568 


79387 


45 


20 


20999 


421 


21578 


78422 


579 


79001 


40 


25 


21382 


411 


21971 


78029 


589 


78618 


35 


30 


21'761 


400 


22361 
9.22747 


77639 


600 


78239 


30 


35 


9.22137 


9.S9390 


10.77253 


10.00610 


10.77863 


25 


40 


22509 


379! 23130 


76870 


621 


77491 


20 


45 


22878 


368 23510 


76490 


632 


77122 


15 


50 


23244 


357 23887 


76113 


643 


76756 


10 


55 


23607 


346 24261 


75739 


654 


76393 


5 


60 


23967 


335 


24632 


75368 


665 


76033 





M 


C. Sine 


Sine 


C.Tang 


Tang. 'C. Sec. 


Secant 


M 


80 Degrees. 


10 Degrees. 


M 


Sine 


C. Sine 


Tang. 


C.Tang. 


Secant 


C. Sec. 


M 

60 





9.23967 


9.99335 


9.24632 


10.75368 


10.00665 


10.76033 


5 


24324 


324 


25000 


75000 


676 


75676 


55 


10 


24677 


313 


25366 


74635 


687 


75323 


60 


15 


25028 


301 


25727 


74273 


699 


74972 


45 


20 


25376 


290 


26086 


73914 


710 


74624 


40 


25 


25721 


278 


26443 


73557 722 


74279 


35 


30 


26063 


267 


26797 


73203 733 


73937 


30 
25 


35 


9.26403 


9.99255 


9.27148 


10.72852 10.00745 


10.73597 


40 


26739 


243 


27496 


72504 757 


73261 


20 


45 


27073 


231 


27842 


721581 769 


72927 


15 


50 


27405 


219 


28186 


718141 781 


72595 


10 


55 


2773.1 


207 


28527 


71473! 793 


72266 


5 


60 


28060 


195 


28865 


71135 
Tang. 


806 


71940 



M 


M 


C. Sine 


Sine 


C.Tang. 


C. Sec. 


Secant 






79 Degrees. 
nBegrees. 










M 


Sine 


C. Sine 
9.99195 


Tang. C.Tang., Secant 


C. Sec. 


M 





9.28060 


9.28865 


10.71135 


10.00805 


10.71940 


60 


5 


28384 


182 


29201 


70799 


818 


71616 


55 


10 


28705 


170 


29535 


70465 


830 


71295 


50 


15 


29024 


157 


29866 


70134 


843 


70976 


45 


20 


29340 


145 


30195 


69805 


855 


70660 


40 


25 


29654 


132 


30522 


69478 


868 


70346 


35 


30 
85 


29966 
9.30275 


119 


30846 


69154 


881 


70034 


30 

25 


9.99106 


9.31168 


10.68832 


10.00894 


10.69725 


40 


30582 


093 


31489 


68511 


907 


69418 


20 


45 


30887 


080 


31806 


68194 


920 


69113 


15 


50 


31189 


067 


32122 


67878 


933 


68811 


10 


55 


31490 


054 


32436 


67564 


946 


68510 


5 


60 

M 


31788 


040 


32748 


67252 


960 


68212 





C. Sine 


Sine 


C.Tang. 


Tang. IC. Sec. 


Secant M| 


78 Degrees. | 



.Mrtijicial Sines, Tangents, and Secants. 25 ^ 





12 Degrees. 


. 


M 


Sine 


C. Sine 


Tang. jC.TangJ Secant 
9.32747110.67253 10.00960 


C. Sec.| 


M 





9.31788 


9.99040 


10.682121 


60 


6 


32084 


99027! 33057 669431 00973 


67916 65 


10 


32378 


99013 33365 66635 00987 


67622 50 


15 


32670 


99000' 33670 66330; 01000 


67330 45 


20 


32960 


98986 33974 66026 


01014 


67040 


40 


25 


33248 


98972' 342761 65724 


01028 


66752 


35 


30 


33534 


98958 


345761 65424 
9.34874! 10.66126 


01042 


66466 


30 

25 


35 


9.S3818 


9.98944 


10.01056 


10.66182 


40 


34100 


98930 


35170 64830 


01070; 65900 


20 


45 


34380 


98916 


35464 64536 


01084! 65620 


16 


50 


34658 


98901 


35757 64243 


01099! 65342 


10 


55 


34934 


98887 


36047 63953 


01113 65066 


5 


60 


36209 


98872 


36336 


63664 


01128 64791 



M 


-M 


C. Sine 


Sine 


C.Tang. 


Tang. 


C. Sec. Secant 




77 Degrees. 




13 Degrees. \ 


Mi Sine 


C. Sine 


Tang. 
9.36336 


C.Tang. 


Secant 
10^1128 


C. Sec; Mi 


9.36209 


9.98872 


10.63664 


10.64791 60 


5 


35482 


98858 


36624' 63376 


01142 


64518 55 


10 


35752 


98843 


36909| 63091 


01157 


64248 50 


15 


36022 


98828 


37193; 62807 


01172 


63978 45 


20 


36289 


98813 


37476i 62524! 01187 


63711 40 


25 


36555 


98798 


37758 62244 


01202 


63445 35 


30; 36818 


98783! 38035! 61965 
9.98768' 9.38313 10.61687 


01217 


63182 30 


35 9.37081 


10.01232 


10.629191 25 


40 


37341 


98733! 38589 


61411 


012471 62659! 20i 


45 


37600 


98737 


38863 


611371 01263! 62400 15 


60 


a785S 


98722 


89136 


60864; 01278 62142 10 


55 38113 


98706 


39407 


60593 01294 61887 5 


60 38368 


98690 


39677| 60323 013101 61632] O] 


M C. Sine 


Sine iC.TangJ Tang. ;C. Sec! Secant 1 M] 


76 Degrees. | 






14 Degrees. | 


M 


Sine 


C. Sine 


Tanar. |C. Tang,' Secant :C. Sec.j Mj 


0, 9.38368 


9.98690 


9.39677| 10.60323 10.01^10 10.61632 


60 


6 


38620 


98875 39945' 60055; 01323, 61380 


55 


10 


38371 


98659 40212; 59783 01341 61129 


50 


15 


39121 


98643 40478 595221 013571 60879 


45 


20 


39369 


98627 40742 


59253; 01373, 60631 


40 


25 


39615 


98610 41004 


589981 01390, 60385 


35 


301 89860 


98594 
9.98678 


41266 


58734} 01406, 601401 30; 


35! 9.40104 


9.41526 


10.58474 10.01422 i0.59896i 25 


40 


40345 


98561 


41784 532161 01439; 596551 20 


45 


40586 


98545 


42042 57958 014551 59414 15 


5C 


40325 


98528 


42297 57703 01472 591751 10 


55; 41063 


98511 


42552 574481 01489 58937 


6 


60' 41300 


98494 
Sine 


42805: 67195; 01508 58700 
C.Tang.l Tang. iC. Sec.l Secant 




"m 


M 


C. Sine 


75 Degrees. \ 



36 Artificial Sines, Tangents, and SecanU, 



15 Degrees. , 


M 




Sine 
9.41300 


I C. Sine 


Tang. 


C.TangJ Secant 
10.5719610.01506 


C. Sec. 


M 


i 9.98494 


9.42805 


10.58700 


60 


5 


41535 98477 


43057 56943 


01523, 58465 


66 


10 


41768' 98460 


*43308 56692 


01540 58232 


50 


15 


42001 98443 


43558; 56442 


01557 67999 


45 


20 


42232 98426 


43806i 56194 


01574 67768 


40 


25 


42462 98409 


44053: 56947 


01591 57538 


35 


30 


42690 98391 


44299 


65701 


01609 


57310 
10.67083 


SO 

26 


35 


9.42917 9.98374 


9.44544 10.66456! 10.01626 


40 


43^143 98356 


44787 56213 


01644 56867 


20 


45 


43368 98338 


46029 54971 


01662 66632 


16 


50 


43591 98320 


45271 64729 


01680 66409 


10 


55 


43813 98302 


46511 64489 


01698 66187 


5 


60 


44034 98284 


45750 
C.Tang. 


54250 


01716 66966 




M 


M 


C. Sine Sine 


Tang. IC. Sec. Secant 


74 Degrees. 


16 Degrees. 


M 


Sine 


C. Sine 


Tang. 1 C.Tang. 


Secant 


C. Sec. 


M 





9.44034 


9.98284 


9.45750 10.54250 


10.01716 


10.66966 


60 


5 


44253 


98266 


45987 


54013 


01734 


55747 


55 


10 


44472 


98248 


46224 


63776 


01752 


65523 


60 


15 


44689 


98229 


46460 


63540 


01771 


65311 


45 


20 


44905 


98211 


46694 


63306 


01789 


56096 


40 


25 


45J20 


98192 


46928 


63072 


01808 


54880 


36 


30 


46334 


98174 


47160 


62840 


01826 


64666 


30 

25 


36 


9.45547. 9.98155 


9.47392; 10.62608 10.01845 10.54453 


40 


457581 98136 


47622 


623781 01864 64242 


20 


45 


45969J 98117 


47852 


62148 


01883| 64031 


15 


60 


461 78J 98098 


48080 


61920 


019021 53822 


10 


65 


46386| 98079 


48307 


61693 


01921 63614 


.6 


60 


465941 98060 


48534 


51466 


01940 53406! O] 


M 


C. Sine! Sine 


C.Tang. 


Tang. C. Sec. Secant i MJ 


73 De 


grees. | 


17 Degrees. | 


Mi Sine 


C. Sine Tang. C.Tang. Secant 
9.98060 9.4863410.51466 10.01940 


C. Seci M. 


9.46594 


10.634061 60 


6 


46800 98040 48759 51241 : 01960 53200; 55j 


10 


47005 


98021! 48984! 51016 


01979 62995 


50 


15 


47209 


980011 49207 50793 


01999 52791 


45 


20 


/ 47412 


97982| 49430 50570 


020181 52688 


40 


25 


47613 


97962^ 496521 50348 


02038 52387 


35 


30 


47814 


979421 


49872 50128! 02058 
9.50092 10.49908 '10.02078 


52186 


30 


35 


9.48014 


9.97922 


10.51986 


25 


40 


48213 


97902 50311 49689 


02093, 51787 


20 


45 


48411 


97882 505291 49471 


02118! 51589 


15 


5a 


48608 


97861' 50746; 49254 


02139! 51392 


'§ 


65 


48803 


97841 50962 49038 


02159' 61197 


60 


48998 


97821 51178 48822 
r Sine C.Tang. Tang. 


02179 51002 


"M 


M C. Sine 


C. Sec. Secant 


72 Decrees. I 



Artificial Sines, Tangents, and Secants. ^T 



18 Degrees. , 


M 


Sine 1 C. Sine; 


Tang. C.Tang. Secant C. See.; Ml 





9.4899a 9.97821. 


9.6117810.4882210.02179 10.51002 SO! 


5 


49192 


97800, 61S92 48608 02200 50808 551 


10 


49385 


97779j 51606 48394; 02221 


60615. 50 
60423 45 


15 


49677 


97759] 51819 48181 02241 


20 


49768 


97738 62031] 47969 02262 


50232 4€ 


25 


49968 


97717i 52242 • 47758 02283 


60042 35 


30 


50148] 


97696| 62452 47548- 02304 


49852 


30j 


35 


9.50336 


9.97674 9.62661 10.47339 10.02326 10.49664 


25| 


40 


60523, 97653 52870, 47130. 02347 


4a477, 20 


45 


50710! 976321 53078 46922] 02368 


492901 15 


SO 


50896 97610 63285, 46716| 02390 


49104] 10 


65 


51080 97589, 534921 465081 02411 


48920 5 


60 61264 


97567] 53697! 46303; 02433 
Sine C.Tang. Tang. iC. Sec, 


48736j 





M' C. Sine 


Secant \ 


M 


71 Degrees. 


19 Degrees. 


IVI| Sine | 


C.Sine, Tang. 


C.Tang. Secant 
10.46303 10.02433 


C. Sec. 


M 

60 


9.51264i 


9.97567 9.53697 


10.48736 


5 


51447 


97545 


53902 


46098 


02455 


48553 


55 


10 


61629 


97523 


64106 


45894 


02477 


48371 


50 


15 


61811 


97501 


64309 


45691 02499 


48189 


45 


20 


61991 


97479 


54512 


45488 02521 


48009 


40 


25 


62171 


97457 


54714 


45286 02543 


47829 


35 


30 


52350 


97435 


54916 


46085 02565 


47660 


SO 
25 
20 


35 


9.52527 


9.97412 


9.55115 


10.44885; 10.02588 


10.47473 


40 


62705 


97390j 55315 


44685 


02610 


47295 


45 52881 


97367 


55514 


44486 


02633 


47119 


15 


50 53066 


97344 


55712 


44288 


02656 


46944 


10 


55 63231 


97322 


55910 


44090 


02676 


46769 


5 


60 5S405 


972991 56107 


43893 


02701 
C. Sec. 


46595 



M 


M C. Sine 


Sine C.Tang 


Tang. 


Secant 


70 Degrees. 


20 Degrees. 


M| Sine 


C. Sine Tang. C.Tang. Secant C. See.j Ml 
9.97299 9.56107 10.4389310.0270110.46595] 6oi 


0; 9.53405 


51 63578 


97275 56303 43697 1 02725; 46422 


55 


10 63751 


97252 66498] 43502; 02748 


46249 


60 


15 53922 


97229] 56693 


43307, 02771 


46078 


45 


20 54093 


97206' 56887 


43113 


02794 


46907 


49 


25 64263 


97182 


57081 


42919 


02818 


45737 


35 


30^ 54433 


97159 


57274 


42726 


02841 


45667 


.30 

25 


3£ 


9.54601 


9.97135 


9.57466 10.42534110.02865 


10.45399 


40 


54769 


97111! 57658 42342] 02889 


45231 


20 


4fi 


54936 


970871 57849] 42151 


0291S 


45064 


15 


5C 


55102 


97063] 58039 41961 


02937 


44898 


10 


5i 


55268 


97039] 58229: 41771 


0296] 


44732 


5 


601 55433 


97015[ 58418) 41682 
Sine C.Tang. Tang. 


0298S 
C. Sec 


44567 



M 


M C. Sine 


1 Secant 


69 Degrees. | 



2S Ariijicial Sines, Tangenfa, and Sedanis. 



21 Degrees. | 


m 


Sine 


C. Sine 


Tang. 


C.Tang. 


Secant 


C. Sec. 


M 





». 55433 


9.97015 


9.68418 


10.41582 


10.02985 


10.44567 


60 


5 


55597 


96991 


58606 


41394 


03009 


44403 


55 


10 


55761 


96966 


58794 


41206 


03034 


44239 


50 


15 


55923 


96942 


58981 


41019 


03058 


44077 


4^ 


20 


56085 


96917 


69168 


40832 


03083 


43915 


40 


25 


56247 


96893 


69354 


40646 


03107 


43753 


36 


30 


56408 


96868 
9.96843 


59540 


40460 


03132 


43592 


3Q 


35 


9.56568 


9.59725 


10.40276 


10.03157 


10.43432 


26 


40 


56727 


968181 69909 


40091 


03182 


43273 


20 


46 


56886 


967931 60093 


39907 


03207 


43114 


15 


50 


57044 


96767' 60276 


39724 


03233 


42956 


1? 


56 


67201 


96742 60459 


39541 


03258 


42799 


I 


60 


57358 


96717 60641 


39359 


03283 


42642 



M 


M 


C. Sine 


Sine C.Tang.' Tang. 'C. Sec.l Secant 


68 Deg;rees. 


22 Degrees. 


M| Sine 


C. Sine 


Tang. 


C.Tang. Secant 


C. Sec. 


M 
60 





9.57358 


9,96717 


9.60641 


10.39359 


10.03283 


10.42642 


5 


57514 


96691 


60823 


39177 


03309 


42486 


56 


10 


57669 


96665 


61004 


38996 


03335 


42331 


50 


15 


57824 


96640 


61184 


38816 


03360 


42176 


45 


20 


67978 


96614 


61364 


38636 


03386 


42022 


40 


25 


58131 


96588 


61644 


38456 


03412 


41869 


35 


30 


58284 


96562 


61722 
9.61901 


38278 


03438 
10.03465 


41716 
10.41564 


SO 

25 


35 


9.68436 


9.96535 


10.38099 


40 


58588 


96509 


62079 


37921 03491 


41412 


20 


45 


68739 


96483 


62256 


37744] 03517 


41261 


15 


50 


68889 


96456 


62433 


37567 03644 


41111 


10 


55 


59039 


96429 


62609 


37391 03571 


40961 


5 


60 


59188 


96403 


62786 


37216 03597 
Tang. C. Sec. 


40812 
Secant 



M 


Ml C. Sine 


Sine 


C.Tang. 




67 De 


grees. 
grees. 








' 23 De 






M 




Sine 


C. Sine 


Tang. 


C.Tang. 


Secant 


C. Sec. 


60 


9.59188 


9.96403 


9.62785 


10.37215 


10.03597 


10.40812 


6 


59336 


96376 


62961 


37039 


03624 


40664 


55 


■10 


59484 


96349 


63135 


36865 


03651 


40516 


50 


15 


59632 


96322 


63310 


36690 


03678 


40368 


45 


20 


59778 


96294 


63484 


36516 


03706 


40222 


40 


25 


59924 


96267 


63657 


36343 


03733 


4D076 


3S 


30 
35 


60070 


96240 


63830 


36170 


03760 


39930 


30 

25 


9.60215 


9.9621^ 


9.64003 


10.35997 


I0.037b8 


10.39785 


40 


60359 


96185 


64176 


35826 


03815 


39641 


20 


4a 


60503 


96157 


64346 


35654 


03843 


39497 


15 


m 


60646 


96129 


64517 


36483 


03871 


39364 


10 


55 


60789 


96101 


64688 


35312 


03899 


39211 


5 


60 


60931 


96073 


64858 


35142 


03927 


39069 





M 


C. Sine 


Sine 


C.Tang. 


Tang. C. Sec. 


Secant 1 M| 


66 Degrees. 1 



^Iriificial SineSf Tangents^ and Secants, 29 



24 Degrees. | 


M 




Sine 4 
9.60931 


::, Sine Tang. C.Tang. 


Secant C 
0.03927 10 


Sec 


^M 


9.96073 


9.64358 10.35142 : 


.39069 60 


5 


61073 


96045 


65028 34972 


03955; 


38927 55 


10 


61214! 


96017 


65197 34803, 


03983 


38786 60 


15 


61354| 


959S8 


65366 34634' 


040121 


38646 45 


20 


614941 


95960 


65535 34465; 


04040! 


38506 40 


2,5 


616341 


95931 


:€5703' 342971 


040691 


38366 35 


30 


61773| 


95902 658701 34130. 04098] 38227 SOj 
9.958731 9.66038 10.33962 10.04127 10.SS089 25] 


35 


9.61911 


40 


62049 


95844 66204 33796 


04156 


ST951 20 


45 


62186 


95815 66371| 33629! 


04185 


37814 15 


60 


62323 


95786 66537 33463 


04214 


37677 10 


65 


62459| 


95757; 66702' 332981 


04243 


37541 5 


60 


62595I 
C. Sine' 


95728! 66S671 331331 
Sine C.Tang. Tang. 


04272 
C. Sec. 


37405 


Secant M 






65 Degrees. 






25 Degrees. { 


M 


Sine 1 


C. Sine Tang. 1 C.Tang. 
9.95728 9.66867 10.33133 


Secant C 
10.04272 1 


. Sec.i 


M 





9.62595 


3.37405 


60 


6 


62730; 


. 95698 67032i 32988 


04302; 


37270! 65 


U 


' 62865' 


95668 67196; 32804 


04332 


37135' 50 


15 


I 62999! 


95639 67360| 32640 


04381 1 


S700l! 45 


2( 


! 63133 


95609 67524 32476 


043911 


36867: 40 


2a 


' 63266 


95579 67687 32313 


04421 


36734 35 


30 


63398 


95549 67850 32150 
9.95519 9.63012 10.31983 


■04451 36602; 30 
10.04481 la 36469: 25 


35 


9.63551 


4C 


' 63662 


95488! 681741 31826 


04512; 


36338| 20 


45 


; 63794 


95458 


68336,- 31664 


04542 


36206 15 


oC 


639241 


95427 


68497 31503 


04573! 


36076' 10 


5a 


, 64054 


95397 


68658 31342 


04603| 


35946! 5 


6C 


' 64184 
ii C. Sine 


95366 


68318 31182 


04634J 
C. Sec' 


358 16 1 


Sine 


C.Tang. Tang. 


Secant 1 M 


a 




64 Degrees. 








26 Degrees. 






[ Sine i 


C. Sine Tang. C.Tang. 


Secant C. Sec.j M 


( 


) 9.64184 


9.95366 9.6881810.31182 


10.0463410.35816; 60 


, 


) 64313 


95335J 68978 31022 


04665 


35687 55 


i( 


), 64442; 


95304 69133; 30862 


04696 


35558 50 


L 


i 645711 


95273 69298| 30702 


04727 


35429 45 


2( 


1 64693! 


95242 694571 30543 


04758 1 


35302 40' 


o 


5 64S26' 


95211! 69615 30385 


04789 1 


35174 35 


3( 


) 64953 


95179| 69774' 30226 
9.95148 9.69932 10.30068 


04821 1 35047; 30 
10.04852 10.349211 25 


3 


5 9.65079 


4 


65205 


9511t 


) 70089, 2991 J 


; 048841 


34795 20 


4 


5 65331 


9508^ 


1 702471 2975S 


04916' 


34669 16 


5 


65456 


9505s 


I 70404; 29596 


049481 


34544 10 


6 


5! 65580 


950201 70560 29440 


04980! 


34420 


5 


« 


0' 65705 


94988| 707171 29283 
Sine 1 C.Tang. Tang^ 


05012 


34295 


_2 

31 


a 


II C. Sine 


C, Sec! 


Secant 






63 Degrees. 







30 Artificial Sines, Tangents, and Secmts> 



27 Degrees. f 


M 


Sine 1 


C. Sine 
9.94988 


Tang. C.Tang.i Secant i 
9.70717 10.29283 10.05012' 


D. Sec.| MJ 





9.65705 


10.34296 


60 


6 


65828 94956 


70873 29127 


05044 


34172 


55. 


10 


65952 94923 


7:.028 


28972 


05077 


34048 


60 


15 


66075 94891 


71184 


28816 


05109 


33926 


45 


20 


66197 94858 


71339 


28661 


05142 


33803 


40 


25 


66319 94826 


71493 


28507 


05174 


33681 


35 


30 


66441 94793 


71648 


28352 


05207 


33569 


SO 


35 


9.66562 9.94760 9.71802 10.28198 10.05240 10.33438i 25 1 


40 


66682 94727 71955! 28045J 05273 


33318 201 


45 


66803 94694 72109; 27891 05306 


33197 16 1 


60 


66922 94660 72262| 27738 05340 


33078 


10 


55 


67042 94627 72415| 27585 05373 82958 


5 


60 


67161 94593 72567' 27433J 05407] 32839 





m 


C.Sine Sine C. Tang. Tang. C. Sec' Secant 


M 


62 Degrees. 


28 Degrees. 


M 


Sine 1 


C. Sine; Tang. C.Tang. 
9.94593, 9.72567 10.27433 


Secant 
10.05407 


C. Sec, Ml 





9.67161' 


10.32839; 60 { 


5 


67280i 94560 


72720 27280 


05410 


32720l 661 


10 


67398! 


94526 


72872{ 27128 


05474 


32602 


50 


15 


67515| 


94192 


73023! 26977 


05603 


32485 


45 


20 


67633 


94453 


73175 26825 


05642 


32367 


40 


25 


67750 


94424 


73326 26674 


06676 


32250 


35 


30 


67866 


94390 


73476 


26524 
10.26373 


05610 


32134 


30 


35 


9.67982 


9.94356 


9.73627 


10.05645| 10.32018 


26 


40 


68098 


94321 


73777 


26223 


05679! 31902 


20 


45 


68213 


94286 


73927 


26073 


05714 


31787 


15 


50 


68328 


94252 


74077 


25923 


05748 


31672 


10 


65 


68443 


94217 


74226 


25774 


05783 


31557 


o 


60 


68557 


94182 


74375 


25625 
Tang. 


05818 


S1443 



M 


M! C. Sine 


Sine IC.Tang. 


C. Sec! Secant 


61 Degrees. \ 


29 De 


grees. [ 


Mj Sine | C. Sine Tang. 


C.Tang. Secant 


C. Sec.| M 


9.66557 


9.94182 9.74375:10.25625,10.05818 


10.31443 60 


5 


68671 


94147 74524 


254761 05853 


31329 55 


10 


68784 


94112 


74673 


26327 


05888 


31216 50 


15 


68897 


94076 


74321 


25179 


05924 


31103 45 


20 


69010 


94041 


74969 


25031 


05959 


30990' 40 


25 


69122 


94005 


75117 


24883 


06995 


■308781 35 


SO 


69234 


93970 


75264 


24736 


06030 
10.06066 


S0766| 30 


85 


9.69345 


9.93934! 9.75411 


10.24589 


10.30655! 25 


4C 


69456 


93898 


75558 


24442 


06102 


305441 20 


4h 


69567 


93862 


75705 


24295 


06138 


30433| 15 


W 


69677 


93826 


75852 


24148 


06174 


303231 10 


bl 


69787 


93789 


75998 


24002 


0621] 


30213 6 


60 69897 


93763 


76144 


23856 


06247 


30103 p 


M C. Sine 


Sine 


C.Tang 


Tang. 


C. Sec. 


Secant M 


>. 


60 Degrees. ' 



Jtrtijicial Sines, Tangents, and Secants, S I 



30 Degrees. , 


M 


Sine 


C. Sine 


Tang. 


C.Tang; 


Secant. 


C. Sec.| Mj 


G 


9.69897 


8.93753 


9.76144 


10.23856 


10.06247 


10.30103 


60 


5 


70006 


93717 


76290 


23710 


0628S 


29994 


55 


10 


70115 


93680 


76435 


23565 


06320 


29885 


50 


15 


70224 


93643 


7658C 


2342C 


06357 


29776 


45 


20 


70332 


93606 


76725 


23275 


06394 


29668 


40 


25 


70439 


93569 


76870 


23130 


06431 


29561 


35 


30 


70547 


93532 


77015 


22985 


06468 


29453 


30 
"23 


35 9.70654 


9.93495 


9.7715910.22841 


10.06505 


10.29346 


40] 70761 


93457 


77303 


22697 


06543 


29239 


20 


45 70867 


93420 


77447 


22553 


06580 


29133 


15 


60 


70973 


93382 


77591 


22409 


06618 


29027 


10 


55 


71079 


93344 


77734 


22266 


06656 


28921 


5 


60 71184! 
M C. Sine! 


93307 


77877 


22123 


06693 


28816 



M 


Sine 


C.Tang. 


Tang. 


C. Sec. 


Secant 


59 Degrees. | 






31 De 


grees. 




M; Sine 


C. Sine 


Tang. C.Tang. Secant. C. Sec. 


M 


9.71184 


9.93307 


9.77877 10.22123 10.06693 10.28816 60| 


5| 71289 


93269 


78020 21980 


06731' 28711 55 


10 713931 


93230 


78163] 21837 


06770] 28607 50 


15 71498 


931C2 


78306 21694 


06808 285021 45 


20| 71602 


93154 


78448 


21552 


06846 


28398 40 


25, 71705 


93115 


78590 


21410! 068S5 


28295 35 


30' 71809 


93077 
9.93038 


78732 21268 06923 


281 91 30 


35 9.71911 


9.78873 10.21126:10.06962]l0.28089 25| 


40, 720141 


92999 


79015 


20985 07001 


27986 20 


45\ 72116 


92960 


79156 


20844 07040 


27S84' 15 


501 72218' 


92921 


79297 


20703 07079 


27782 10 


55l 72320 


92881 


79438 


20562 07119 


27680] 5 


60l 72421' 


92842 
Sine 


79579 
C.Tang. 


20421 07158 


27579' 


M C. Sine 


Tang. C. Sec. 


Secant. M 


58 De 


grees^___ 
;rees. 










32 be, 






M Sine [ 


C. Sine 


Tang. C.Tang. Secant C. Sec. 


M 


9.72421, 


9.92842 


9.79579 10.20421 10.07158 10.27579 60 


5 


72522 


92803 


79719i 20281; 071971 27478 56 


10 


72622 


92763 


79860 20140i 07237 


273781 50 


15 


72723 


92723 


80000 


20000 


07277 


27277 45 


20 


72823 


92683 


80140 


19860 


07317 


27177 40 


25 


729221 


92643 


80279 


19721 


07357 


27078 35 


30 
35 


73022 
9.731211 


92603 
9.92563 


80419 
9.80558 


19581 
10.19442 


07397 


26978! 


301 


10.07437 


10.26879' 


25 


40 


73219 


92522 


80697] 19303 


07478 26781! 20 


45l 73318' 


92482 


80836 19164 


07518 26682] 15 


50 73416] 


92441 


80975 


19025 


07559 26584 10 


55 73513' 


92400 


81113 


18887 


07600 264871 5 


€0 73611 
I^ri C. Sine 


92359 
Sine 


81252 


18748 


07641 
C. Sec. 


263891 01 


C.Tang. 


Tang. 


Secant 1 Ml 








57 Degrees. .. „ 1 



^S2 *^rUJicial Sines, Tangents, and Secants. 



33 Degrees. i n-j 


M 




Sine 


C. Sine 


Tang. 


C.Tang. 


Secant C. Sec. 


M 

60 


9.73611 


9.92359 


9.81252 


10.18748 


10.07641 10.26389 


6 


73708 


92318 


81390 


18610 


07682 


26292 


55 


10 


73805 


92277 


81628 


18472 


07723 


26195 


50 


15 


73901 


92235 


81666 


18334 


07765 


26099 


45 


20 


73997 


92194 


81803 


18197 


07806 


26003 


40 


25 


74093 


92152 


81941 


18059 


07848 


25907 


35 


30 
35 


74189 
9.74284 


92111 


82078 


17922 


07889 


25811 


30 


9.92069 


9.82216 


10.17785 


10.07931 


10.25716 


25 


40 


74379 


92027 


82352 


17648 


07973 


25621 


20 


45 


74474 


91985 82489 


17511 


08016 


25526 


15 


50 


74568 


91942! 82626 


17374 


08058 


26432 


10 


55 


74662 


91900 82762 


17238 


08100 


25338 


6 


60 
M 


74756 


91857 
Sine 


82899 


17101 


08143 


25244 




M 


C. Sine 


C.Tang. 


Tang. 


C. Sec. 


Secant 




56 Degrees. | 


34 Degrees. | 


M 


Sine 


C. Sine Tang. | 


C.Tang. 


Secant 


C. Sec. M| 





9.74756 


9.91857 


9.82899 


10.17101 


10.08143 


10.25244 


60 


5 


74850 


91815 


83035 


16965 


08185 


25150 


55 


10 


74943 


91772 


83171 


16829 


08228 


25057 


50 


15 


75036 


91729 


83307 


16693 


08271 


24964 


46 


20 


75128 


91686 


83442 


16558 


08314 


24872 


40 


25 


75221 


91643 


«3578 


16422 08357 


24779 


35 


30 


75313 


91599 


83713 


16287 08401 


24687 


30 

25 


35 


9.75405 


9.91556 


9.83849 


10.1615110.08444 


10.24595 


40 


75496 


91512 


83984 


16016 08488 


24504 


20 


45 


75587 


91469 


84119 


15881 08531 


24413 


15 


50 


75678 


91425 


84254 


16746 08575 


24322 


10 


00 


75769 


91381 


84388 


15612 08619 


24231 


6 


60 


75859 


91336 


84523 


15477 
Tang. 


08664 


24141 





M 


C. Sine 


Sine 


C.Tang. 


C. Sec' Secant 


M 




55 De 


jrees. 

grees. 




35 De 




M 




Sine 


C. Sine 


Tang. 


C.Tang., Secant 


C. Sec. 


M 


9.75859 


9.91336 


9.84523 


10.15477 


10.08664 


10.24141 


60 


5 


75949 


91292 


84657 


15343 


08708 


2405] 


56 


10 


76039 


91248 


84791 


15209 


08752 


23961 


50 


15 


76129 


91203 


84925 


15075 


C8797 


23871 


45 


20 


76218 


91158 


85059 


14941 


08842 


23782 


40 


25 


76307 


91114 


85193 


14807 


08886 


23692 


35 


30 


76395 


91069 


85327 


14673 


08931 


23605 


30 


35 


9.76484 


9.91023 


9.85460 


10.14540 


10.08977 


10.23516 


25 


40 


76572 


90978 


85594 


14406 


09022 


23428 


20 


45 


76660 


90933 


85727 


14273 


09067 


23340 


15 


50 


76747 


90887 


85860 


14140 


09113 


23253 


10 


55 


76835 


90842 


85993 


14007 


09158 


23165 


5 


60 
M 


76922 


90796 


8612a 


13874 


09204 


23078 





C. Sine 


Sine 


C.Tang. 


Tang. iC. Sec. 


Secant 


M 




54 Degrees. ^ \ 



Jtrtificial Sines, Tangents, and Secariits. 33 



3S^ Degrees. 



Sine 



9.76922 
77009 
'77095 
77181 
77268 
77353 
77439 



C. Sine 



9.90796 
90750 
90704 
90657 
90611 
90565 
90518 



9.77524 9.90471 
776091 90424 



77694: 

77778j 
778621 
77946 



Tang. 



C.Tang. Secant iC. Sec. M 



9.86126 
86259 
86392 
86524 
86656 
86789 
86921 



10.1337410.0920410, 

13741 09250 

13608 09296 

13476 09343 

13344 09389 

132111 09435 

13079; 09482 



23078 60 
22991 66 
22305 50 
22819 45 
22732' 40 
22647 35 
225611 30 



90377 
90330 
90282 
90235 



Ml C. Sine Sine 



9.87053,10.12947 10.09529 
87185 12815 09576 
873171 12683, 09623 
874431 12552 09670 
87580; 12420 09718 
877111 12289 0976, 



10.22476 25 
22391 20' 
22306 15 
22322 10 
22136; 5 
22054 



C.Tang.' Tang. C. Sec. 



Secant I M 



53 Degrees . 
37 Degrees. 



Ml Sine 



9.77946 
78030 
78113 
78197 
78280 
78362 
78445 



9.78527 
78609 
77691 

78772 
78853 
789341 



C. Sine, Tang. iC.Tang.l Secant ,C. Sec.i M 



9.90235 
90187 
90139 
90091 
90043 
89995 
89947 



89849 
89801 
89752 
89702 
89653 



9.87711110.12289 10.0976510.220541 60 

21970 65 

21687 50 

21803 45 

21720 40 

21638 35 

21555 SO 



87843 
87974 
88105 
88236 
88367 
88498 



121571 
12026 
11895 
11764 
11633 
115(B 



098131 
09861 
09909! 
09957 
10005! 
100531 



9.88629 10. 1 1371 110.10102 10.21473 



88769 
88890 
89020 
89151 
89281 



112411 
11110 

10980 
10849 
10719 



10151 I 

10199 
10248! 
10298J 
103471 



21391 
21309 
21228 
21147 
210661 



C. Sine! Sine IC.Tang.l Tang. IC. Sec.: Secant I M 



62 Degrees. 



38 Degrees. 



Sine I C. Sinej Tang^jC.Tang. Secant C. Sec.j M 

60 



9.78934 
79015 
79095' 
791761 
79256. 
79335! 
79415 



9.89653 
896041 
895541 
895041 
894351 
89405| 
S93541 



9.8928110.10719 10.10347 10.21066 
20985 
20905 
20824 
20744 
20385 
205S5 



89411 


10589 


10396 


89541 


10459 


10446 


89671 


10329 


10496 


89801 


10199 


10545 


89931 


10069 


10595 


90061 


09939 


10646 



9.79494 9.893041 9.90190 10.09810 10. 10696 10.205061 
79573, 892541 90320 09680 10746- 20427^ 
796521 892031 90449! 09551 107971 20348 
797311 89152 90578 09422 108481 20269 
79809, 89101 90708 09292 108991 20191 
79887 89050 | 90837 1 09163 _J^^\_J^\^ 

C. Sine! Sine C.Tang. Tang. IC. Sec. i Secant 
51 D egrees. 

8 



55! 
5() 

45 
40| 
35 i 
J10| 
25^ 
20] 
15 
10 3 

_oi 

mI 

— « 



34 .Artificial Sines, Tangents, and Secants^ 





39 Degrees. 


"" 


M 


Sine 


C. Sine 


Tang. C.Tang., Secant) 


C. Sec. 


M 

60 





9.79887 


9.89050 


9.90837 


10.09163 


10.10950 


10.20113 


6 


79965 


88999 


90966 


09034 


11001 


20035 


55 


10 


80043 


88948 


91095 


08905 


11062 


19957 


60 


16 


80120 


88896 


91224 


08776 


H104 


19880 


45 


20 


80197 


88844 


91353 


08647 


11156 


19803 


40 


25 


60274 


88793 


91482 


08618 


11207 


19726 


35 


30 


80351 


88741 


91610 


08390 
10.08261 


11259 


19649 


30 


35 


9.80428 


9.88688 9.91739 


10.11312 


10.19572 


25 


40 


80504 


886361 91868 


08132 


11364 


19496 


20 


45 


80580 


88584' 91996 


08004 


11416 


19420 


15 


50 


80656 


88531' 92125 


07875 


11469 


19344 


10 


55 


80731 


88478 92253 


07747 


11522 


19269 


5 


60 
M 


80807 
C. Sine 


88425 
Sine 


92381 


07619 


11575 


19193 



M 


C.Tang. 


Tang. 


C. Sec. 


Secant 


50 Degrees. 


40 Degrees. 


M 


Sine 


C. Sine Tang. jC.Tang. 


Secant 


C. Sec. M| 





9.80807 


9.88425 


9.92381 


10.07619 


10.11575 


10.19193 


66 


5 


80882 


88372 


92510 


07490 


11623 


19118 


55 


10 


80957 


88319 


92638 


07362 


11681 


19043 


50 


15 


81032 


88266 


92766 


072S4 


11734 


18968 


45 


20 


81106 


88212 


92694 


07106 


11788 


18894 


40 


25 


81180 


88158 


93022 


06978 11842 


18820 


35 


30 


81254 


88105 


93150 


06850 11 895 


18746 


30 

25 


35 


9.81328 


9.88050 


9.93278 


10.0672210.11950 


10.18672 


40 


81402 


87996 


93406 


06594 12004 


18598 


20 


45 


81475 


87942 


93533 


06467 12053 


18525 


15 


50 


81549 


87887 


93661 


06339 12113 


18451 


10 


55 


81622 


87833 


93789 


06211: 12167 


18378 


5 


60 


81694 


87778 


93916 


060S4 
Tang. 


12222 


18306 



M 


M 


C. Sine 


Sine C.Tang. 


C. Sec.l Secant 








49 Degrees. 
41 Degreielt 


1 












M 


Sine 


C. Sine 


Tang. 
9.93916 


C.Tang., Secant 


C. Sec. 


M 





9.81694 


9.87778 


10.06084 


10.12222 


10.18306 


60 


5 


81767 


87725 


94044 


06956 


12277 


18233 


65 


10 


81839 


87668 


9417] 


05829 


12332 


18161 


SO 


15 


8191] 


8761S 


9429£ 


05701 


12381 


18089 


45 


20 


8198f 


87557 


94426 


0557-^ 


12443 


J8017 


40 


26 


82055 


87501 


9455^ 


05446 


12499 


17945 


36 


30 


82126 


87446 


94681 


05319 


12554 


17874 
10.17802 


30 

25 


35 


9.82198 


9.87390 


9.94808 


10.05192 


10.12610 


40 


82269 


87334 


94936 


05065 


12666 


17731 


20 


45 


8234C 


87277 


95062 


04938 


12723 


17660 


15 


6C 


8241C 


87221 


95190 


04810 


12779 


17590 


10 


5i 


8248] 


87164 


95317 


04683 


12836 


17519 


6 


6C 


) 8255 


87107 


96444 


04556 


12893 


17449 



M 


M' C. Sine 


Sine 


C.Tang 


Tang. 


IC. Sec. 


Secant 


I 


48 Degrees. _ \ 



Artificial Sines, Tangents, and Secants. 35 



42 Degrees. | 


M\ Sine C. Sine 


Tang. 


C.Tang. 


Secant. 


C. Sec. 
10.17449 


IVI 

60 


6 9.82551 9.87107 


9.95444 


10.04556 


10.12893 


5 82621 87050 


95571 


04429 


12950 


17379 


.W 


10 82691 


86993 


95698 


04302 


13007 


17309 


60 


15 82761 


86936 


95825 


04175 


13063 


17239 


45 


20 8-2830 


86879 


95952 


04048 


13121 


17170 


40 


25 82899 


86821 


96078 


03922 


13179 


17101 


35 


30 82968' 86763 


96205 


03795 


13237 


17032 


30 
15 


85 9.83037: 9.86705 9.96332 


10.03668 


10.13295 


10.16963 


40 83106J 8S647 96459 03541 


13353 


168941 20] 


45 831741 86589 96586 03414 


13411 


16826 


15 


60 83242i 86530 96712 


03288 


13470 


16758 


10 


55 83310! 86472 96839 


03161 


13528 


16690 


6 


60 833781 86413 96966 


03034 13587 


16622 





Ml C. Siael Sine iC.Tang.! Tang. IC. Sec. 


Secant i Ml 


47 Degrees. 


! 


43 Degrees. 






M Sine | C. Sine; Tang. iCTan^. 


Secant. C. Sec. 


M 





9.833781 9.86413 9.96966, ia03034 10.13587,10.16622 60i 


5 


83446 


86354: 97092 02908 


13646 


16554 65 


10 


83513 


86295| 97219 02781 


13705 


16487: 50 


15 


83581 


86235; 97345 02655 


13765 


164191 45 


20 


83648 


86176, 97472 02528 


13824 


16352 40 


25 


83715 


881161 97598 02402 


13884 


16285 35 


30 83781 


86056j 97725 02275 


13944 


162191 30, 


So 9.83848 


9.85996 9.9785110.02149 10.1400410.161521 25' 


40 


83914 


85936 979781 02022! 14064 


16086 20 


45 


83980 


85876 98104 


01896 14124 


160-20 


15 


50 


84046 


85815 98231 


01769 14185 


15954 


10 


-55 


84112 


857541 98357 


01643 14246 


15888 


a 


60 


84177 


85693 


98484 


01516 14307 


15823 





M! C. Sinel Sine 


'c.Tang. 


Tang. 1 C. Sec. 


Secant, i M>. 


46 D 


egrees. 

agrees. 




44 D 




M| Sine } C. Sine Tang. C.Tang.; Secant C. Sec. M 


Oi 9.84177 9.85393, 9.98484 10.01516 10.14307 10.15823 60 


5 


84-242} 85632: 98610 01390: 14368 15758 55, 


10 


84308 85571: 98737; 01263 14429 


15692 50 


15 


84373' 85510: 98863| 011371 14490 


15627 45 


20 


64437 


85448 98989 


OlOllj 14562 


15563 40 


25 


84502 


85386 99116 


003841 14614 


154981 35 


,30 


84566 


85324 99242 


00758 


14676 
10.14738 


15434! 30 


35 


9.84630' 9.852621 9.99368'10.00632 


10.15370! 25 


40 


846941 8520C 


99495 


00505 


1480C 


15306! 20 


45 


84758| 8513- 


99621 


0037£ 


14863 


152421 15 


6( 


84822 85074 


99747 


0025J 


14926 


15178, 10 


55| S4885 85012 


9987< 


00126 


14988 


15115 5 


60] 84949 8494E 


10.00000 


10.00000 


15051 1 150511^ 
C. Seel Secant ! M, 


Mi C. Sinel Sine 


IC.Tang 


Tang. 








45 D 


egrees. ^ { 



^Q TRAVERSE TABL£. 



Ill, A Traverse Table, or Table of Difference of Latj- 
TUDE AND Departure, calculated for degrees and quarters of 
degrees, and for any distance up to 100 Rods, Chains, &c. ; by 
which the northings and southings, eastings and westings made 
in a Survey may be found. 

JVote. Northings and southings are called Difference of Latitude, or simply 
Latitude ; eastings and westings are called Departure, Meridian Dis- 
tance, or Longitude. 

Explanation of the Table. 

To find the Latitude and Departurcf or Worthing, Sj-c. for any 
Course and Distance. 

If the Course be less than 450, look for it at the top, but If 
more than 45° at the bottom of the page, and look for the Dis- 
tance in the right or left hand column ; against the Distance, 
^"hd directly under or over the Course, stand the norUiing, &c. 
in whole numbers and decimals. 

If the Course be less than 45°, the northing or southing will 
be greater than the easting or westing; but if more than 450. 
the easting or westing will be the greatest. 

When the Distance exceeds 100, take any two or more num- 
bers, which, added together, will equal the Distance, and find 
the Latitude and Departure for each of those numbers ; add 
the several Latitudes together and the sum will be the whole 
Latitude ; and so for the Departure. And when the Distance 
is in Chains and I^inks, or whole numbers and decimals, find 
the Latitude, &c. for the Chains or whole numbers, and then 
for the Links or decimals, remembering to remove the decimal 
point in the Table further to the left, according to the given 
"decimal. 

Examples. 

J. Required the Latitude and Departure for 45 Rods, on a 
Course JV. 150 15^ W. 

Under 15° 15^ and against 45 is 43.42 for the northing, and 
11-. 84 for the westing. 

2. Required the Latitude and DepaTtute for 1 20 Rods, on « 
Course S. Sgo 30^ J5. 



TRAVERSE TABLE. 37 

Take one third of 120 which is 40 ; against this number, 
over 58« 30' is 29.90 for the Latitude and 34.11 for the De- 
parture. These muhiplied by 3 give G2.70 for the Southing 
and 102.33 for the Easting. 

3. Required the Latitude and Departure for 37.36 Rods or 37 
Chains and 36 Links, on a Course JV. 26** 46' E. 

For 37. Lat. 33 04 Dep. 16.65 

0.36 .32 .16 



37.36 33.36 16.81 

Northing 33.36 Easting 16.81 

Xote. When the Minutes are not 15, 30, or 45, the Northings, &c. must 
ISe calculated by Natural Sines, or by Ti'igonometry. 



38 



TRAVERSE TABLE. 



Ed 


"ft)ei. 


i'i)eg. 


ibeg. 


9. 


Lat.lDep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


l.OOj 0.00 


1.00 


0.01 


1.00 


0.01 


1 


2 


2.00i 0.01 


2.00 


0.02 


2.00 


0.03 


2 


3 


3.00 0.01 


3.00 


0.03 


3.00 


0.04 


3 


4 


4.00 0.02 


4.00 


0.03 


4.00 


0.06 


4 


5 


5.00 0.02 


5.00 


0.04 


5.00 


0.07 


5 


6 


6.0a 0.03 


6.00 


0.05 


6.00 


0.08 


6 


7 


7.00i 0.03 


7.00 


0,06 


7.00 


0.09 


7 


8 


8.00 0.03 


8.00 


0.07 


8.00 


0.10 


8 


9 


9.00i 0.04 


9.00 


0.08 


9.00 


0.12 


9 


10 
11 


10.00: 0.04 
11.00 0.05 


10.00 


0.09 


10.00 


0.i3 
0.14 


16 
11 


11.00 


0.10 


11.00 


12 


12.00' 0.05 


12.00 


0.10 


12.00 


0.16 


12 


13 


13.00: 0.06!! 13.00 


0.11 


13.00 


0.17 


13 


14 


14.00 0.06 114.00 


0.12 


14.00 


0.18 


14 


15 


15.00 0.07 


jl5.00 


0.13 


15.00 


0.20 


15 


18 


16.00 0.07 


116.00 


0.14 


16.00 


0.21 


16 


17 


17.00 0.07 


17.00 


0.15 


17.00 


0.22 


17 


18 


18.00 0.08 


18.00 


0.16 


18.00 


0.24 


18 


19 


19.00 0.08 


19.09 


0.17 


19.00 


0.25 


19 


20 


20.00! 0.09 (20.00 


0.17 


20.00 


0.26 


20 


21 


21.00 0.09 21.00 


0.18 


21.00 


0.27 


21 


2222.00 O.lOi 22.00 


0.19 


22.00 


0.29 


22 


23 23.00 0.10123.00 


0.20 


23.00 


0.30 


23 


2424.00 0.10! 24.00 


0.21 


24.00 


0.31 


24 


25 25.00 0.11125.00 


0.22 


25.00 


0.33 


25 


26 26.00 0.11 


26.00 


0.23 


26.00 


0.34 


26 


27 27.00 0.12 


27.00 


0.24 


27.00 


0.35 


27 


28 28.00 0.12 


28.00 


0.24 


28.00 


0.37 


28 


29 29.00 0.13 


29.00 


0.25 


29.00 


0.38 


29 


3030.00 0.13 


30.00 


0.26 


30.00 


0.39 


30 


3131.00 0.14 


31.00 


0.27 


31.00 


0.41 


31 


32 32.00 0.14132.00 


0.28 


32.00 


0.42 


32 


33 33.00 0.14,33.00 


0.29 


33.00 


0.43 


33 


34 34.00 0.15 34.00 


0.30 


34.00 


0.45 


34 


35 35.00 0.15 35.00 


0.31 135.00 


0.46 


35 


36 36.00 0.16 36.00 


0.31 136.00 


0.47 


36 


37 37.00 0.16 37.00 


0.321137.00 


0.48 


37 


38 38.00 0.17 38.00 


0.33 


38.00 


0.50 


38 


39 39.00 0.17139.00 


0.34 


39.00 


0.51 


39 


4040.00 0.17 


40.00 


0.35 


40.00 


0.52 


40 


4141.00 0.18 


41.00 


0.36 


41.00 


0.54 


41 


42 42,00 0.18| 42.00 


0.37 


42.00 


0.55 


42 


43 43.00 0.19 43.00 


0.38 


43.00 


0.56 


43 


44 44.00 0.19 44.00 


0.38 


44.00 


0.58 


44 


45 45.00 0.20 45.00 


0.39 


45.00 


0.59 


45 


46 46.00 0.20l 46.001 0.40| 


46.00 0.601 


46 


47 


47.00 0.21 


47.00 0.41 


47.00 0.62 47 


48 


48.00 0.21 


48.00 0.42 


48.00 0.63 48 


49 


49.00 0.21 


49.00! 0.43 


49.00 0.64 49 


50 


50.00 0.22 


50.00| 0.44 


50.00 0.651 50 




Dep. Lat. 


Dep. Lat. 


Dep. Lat. 


tg 


89|Deg. 


89iDeg. 


89iDeg. 


Q 



TRAVERSE TABLE. 



3Sf 



5 


iDeg. 


iDeg. 


|Deg. 





5 

51 


Lat. 
51.0C 


Dep. 
0.22 


Lat. 


Dep. 


Lat. Dep. 
51.00 0.67 


51 


51.00 


0.45 


52 


52.00 


0.23 


52.00 


0.45 


52.00 


0.68 


62 


53 


53.00 


0.23 


53.00 


0.46 


53.00 


0.69 


53 


64 


54.00 


0.24 


54.00 


0.47 


54.00 


0.71 


64 


55 


55.00 


0.24 


55.00 


0.48 


55.00 


0.72 


55 


56 


56. C6 


0.24 


56.00 


0.49 


56.00 
57.00 


0.73 


56 


57 


57.0C 


0.25 


57.00 


0.50 


0.75 


67 


58 


58.0C 


0.25 


58.00 


0.51 


57.99! 0.76 


58 


59 


59.C(. 


0.26 


59.00 


0.51 


58.991 0.77 


59 


60 
61 


60.0C 
61.CC 


0.26 


60.00 


0.52 


59.99I 0.79 
60.991 0.80 


60 
61 


0.27 


61.00 


0.53 


62 


62.0C 


0.27 


62.00 


0.54 


61.99 


0.81 


62 


63 


63.00 


0.27 


63.00 


0.55 


62.99 


0.82 


63 


64 


■64.00 


0.28 


64.00 


0.56 


63.99 


0.84 


64 


65 


65.0C 


0.28 


65.00 


0.57 


64.991 0.85 


66 


66 


66.CC 


0.29 


66.00 


0.58 


65.99! 0.86 


66 


67 


67.0C 


0.29 


67.00 


0.58 


66.99; 0.88 


67 


68 


68.0C 


0.30 


68.00 


0.59 


67.99' 0.89 


68 


69 


69.0C 


0.30 


69.00 


0.60 


68.99, 0.90 


69 


70 
71 


70.0C 
71.00 


0.31 


70.00 


0.61 


69.99 


0.92 


70 
71 


0.31 


71.0o! 0.62 


70.99 


0.93 


72 


72.0C 


0.31 


72.00' 0.63 


71.99 


0.94 


72 


73 


73.00 


G.32 


73.OO1 0.64 


72.99 


0.96 


73 


74 


74.00 


0.32 


74.00 


0.65 


73.99 


0.97 


74 


75 


75.0C 


0.33 


75.00 


0.65 


74.99 


0.98 


75 


76 


76.00 


0.33 


76.00 


0.66 


75.99 


0.99 


76 


77 


77.0C 


0.34 


77.00 


0.67 


76.99 


1.01 


77 


78 


78.CC 


0.34 


78.00 


0.68 


77.99 


1.02 


78 


79 


79.0t 


0.34 


79.00 


0.69 


78.99 


1.03 


'9 


80 


80.C1 


0.35 


80.00 


0.70 


79.99 


1.05 


80 


81 


81.CC 


0.35 


81.00 


0.71 


80.99 


1.06 


81 


82 


82.00 


0.36 


82.00 


0.72 


81.99 


1.07 


82 


83 


83.tt 


0.36 


83.00 


0.72 


82.99 


1.09 


83 


84 


84.a 


0.37 


84.00 


0.73 


83.99 


1.10 


84 


86 


85.0C 


0.37 


85.00 


0.74 


84.99 


1.11 


85 


86 


86.CC 


0.38 


86.00 


0.75 


85.99 


LIS 


86 


87 87. (A 


0.38 


87.00 


0.76 


86.99 


1.14 


87 


88; 88.U 


C.38 


88.00 


0.77 


87.99 


L15 


88 


891 sg.ot 


0.39 


89.00 


0.78 


88.99 


i.iei 89 


90 90.0C 


0.39 


90.00 


0.79 


89.99 


1.18 90 


91 91.0C 


0.40 


91.00 


0.79 


90.99 


1.19; 91 


92! 92.0C 


0.40 


92.09 


0.80 


91.99 


1.20 


92 


93 93.CC 


0.41 


93.00 


-0.81 


92.99 


1.22 


93 


94' 94.0C 


0.41 


1 94.00 


0.82 


93.99 


1.23 


94 


95 95.0C 


0.41 


95.00 


0.83 


94.99 


1.24 


95 


96, 96.0C 


0.42 


96.00 


0.84 


95.99 


1.26 


9« 


97 97.0C 


0.42 


97.00 


0.85 


96.99 


1.27 97 

1.28 98 


98 98.0C 


0.43 


98.00 0.86 


97.99 


99 99.0C 


0.43 


99.00 


0.86 


98.99 


1.30 99 


100 lOO.OC 


0.44 


100.00 


0.87 


99.99 


1.31 100 


■♦-J 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. Lat.i 


CO 


Q 


89|Deg. 


89iDeg. 1 


89peg.| 


5 



40 



TRAVERSE TABLE. 



o 

1 


1 Deg. 


H Deg. 


1 i Deg. 


l|Deg.| 


2 

So' 

<-► 
1 


Lat. 


Dep. 

0.02 


Lat. 

1.00 


Dep. 
0.02 


Lat. 


Dep. 
0.03 


Lat. 
1.00 


Dep. 
0.03 


1.00 


1.00 


2 


2.00 


0.03 


2.0(? 


0.04 


2.00 


0.05 


2.00 


0.06 


2 


3 


3.00 


0.05 


3.00 


0.07 


3.00 


0.08 


3.00 


0.09 


3 


4 


4.00 


0.07 


4.00 


0.09 


4.00 


0.10 


4.00 


0.12 


4 


5 


5.00 


0.09 


6.00 


0.11 


5.00 


0.13 


6.00 


0.16 


6 


6 


6.00 


0.10 


6.00 


0.13 


6.00 


0.16 


6.00 


0.18 


6 


7 


7.00 


0.12 


7.00 


0.15 


7.00 


0.18 


7.00 


0.21 


7 


8 


8.00 


0.14 


8.00 


0.17 


8.00 


0.21 


8.00 


0.26 


8 


9 


9.00 


0.16 


9.00 


0.20 


9.00 


0.24 


9.00 


0.28 


9 


10 


10.00 


0.17 


10.00 
11.00 


0.22 


10.00 


0.26 


10.00 


0.31 


10 


11 


11.00 


0.19 


0.24 


11.00 


0.28 


10.99 


0.34 


11 


12 


12.00 


0.21 


12.00 


0.26 


12.00 


0.31 


11.99 


0.37 


12 


13 


13.00 


0.23 


13.00 


0.28 


13.00 


0.34 


12.99 


0.40 


13 


14 


14.00 


0.24 


14.00 


0.31 


14.00 


0.37 


13.99 


0.43 


14 


15 


15.00 


0.26 


15.00 


0.33 


14.99 


0.39 


14.99 


0.46 


15 


16 


16.00 


0.28 


16.00 


0.35 


15.99 


0.42 


1.6.99 


0.49 


16 


17 


17.00 


0.30 


17.00 


0.37 


16.99 


0.45 


16.99 


0.62 


17 


18 


18.00 


0.31 


18.00 


0.39 


17.99 


0.47 


17.99 


0.56 


18 


19 


19.00 


0.33 


19.00 


0.41 


18.99 


0.60 


18.99 


0.68 


19 


20 


20.00 


0.35 
0.37 


20.00 
21.00 


0.44 
0.46 


19.99 
20.99 


0.52 


19.99 
20.99 


0.61 


20 
21 


21 


21.00 


0.55 


0.64 


22 


22.00 


0.38 


21.99 


0.48 


21.99 


0.68 


21.99 


0.67 


22 


23 


23.00 


0.40 


22.99 


0.60 


22.99 


0.60 


22,99 


0.70 


23 


24 


24.00 0.42. 


23.99 


0.52 


2.S.99 


0.63 


23.99 


0.73 


24 


26 


25.00 


0.44 


24.99 


0.55 


24.99 


0.65 


24.99 


0.76 


2£ 


26 


26.00 


0.45 


26.99 


0.57 


26.99 


0.68 


25.99 


0.79 


26 


27 


27.00 


0.47 


26.99 


0.59 


26.99 


0.71 


26.99 


0,83 


27 


28 


28.00 


0.49 


27.99 


0.61 


27.99 


0.73 


27.99 


0.86 


28 


29 


29.00 


0.61 


28.99 


0.63 


28.99 


0.76 


28.99 


0.89 


29 


30 
31 


30.00 


0.52 


29.99 


0.66 

- 


29.99 


G.79 


29.99 


0.92 


30 


31.00 


0..54 


30.99 


0.68 


30.99 


0.81 


30.99 


0.95 


31 


32 


32.00 


0.,56 


31.99 


0.70 


31.99 


0.84 


31.99 


0,98 


32 


33 


32.99 


0.58 


32.99 


0.72 


32.99 


0.86 


32.98 


1,01 


33 


34 


33.99 


0.59 


33.99 


0.74 


33.99 


0.89 


33.9S 


1,0< 


S4 


35 


34.99 


0.61 


34.99 


0,76 


34.99 


0.92 


34.98 


1,07 


35 


36 


35.99 


0.63 


36.99 


0.79 


35.99 


0.94 


35.98 


I.IC 


36 


37'36.99 


0.65 


36.99 


0.81 


36.99 


0.97 


36.98 


l.U 


37 


38i37.99 


0.66 


37.99 


0.83 


37.99 


0.99 


37.98 


1.16 


38 


39:38.99 


0.68 


38.99 


0.85 


38.99 


1.02 


38.98 


L19 


39 


40 


39.99 


0,70 


39.99 


0.87 


39.99 


1.05 


39.98 


1.22 


40 
41 


41 


40.99 


0.72 


40.99 


0.89 


40.99 


1.07 


40.98 


1.2S 


42141.99 


0.73 


41.99 


0.92 


41.99 


1.10 


41.98 


1.2f 


42 


43142.99 


0.75 


42.99 


0.94 


42.99 


1.13 


42.98 


1.3 


43 


44143.99 


0.77 


43.99 


0.96 


43.99 


1.15 


43.98 


1.3< 


44 


45 44.99 


0.79 


44.99 


0.98 


44.99 


1.18 


44.98 


1.37 


45 


46 45.99 


0.80 


45.99 


1.00 


45.99 


1.20 


46.98 


1.40 


46 


4746.99 


0.82 


46.99 


1.03 


46.39 


1.23 


46.98 


1,4; 


47 


48 47.99 


0.84 


47.99 


1 06 


47.98 


1.26 


47.98 


1.47 


48 


49 48.99 


0.86 


48.99 


1.07 


48.98 


1.28 


48.98 


1,5C 


49 


60 49.99 


0.87 
Lat. 


49.99 


1.09 
Lat. 


49.98 
Dep. 


1.31 


49.98 


1,53 


60 

en 

Q 


"S 


Dep. 


Dep. 


Lat. 


Dep. 


Lat. 


Q 


|89 Deg. 


88|Deg. 


Upeg. 


88iDeg. 



TRAVERSE TABLE. 



41 



d 
p. 

51 


1 Deg. 


1^ Deg. 


HDeg. 


11 Deg. 


CO 

51 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




50.99 


0.89 


50.99 


1.11 


50.98 


1.34 


50.98 


1.56 




52 


51.99 


0.91 


51.99 


1.13 


51.98 


1.36 


51.98 


1.59 


52 




53 


52.99 


0.92 


52.99 


1.16 


52.6-8 


1.39 


,52.98 


1.62 


53 




54 


W.99 


0.94 


53.99 


1.18 


53.98 


1.41 


,53.97 


1.65 


54 




55 


54.99 


0.96 


54.99 


1.20 


54.98 


1.44 


54.97 


1.68 


55 




56 


55.99 


0.98 


55.99 


1.22 


55.98 


1.47 


55.97 


1.71 


56 




57 


56.99 


0.99 


56.99 


1.24 


56.98 


1.49 


56.97 


1.74 


57 




58 


57.99 


1.01 


57.99 


1.27 


57.98 


1.52 


57.97 


1.77 


58 




59 


58.99 


1.03 


58.99 


1.29 


58.98 


1.54 


,58.97 


1.80 


59 




60 
61 


59.99 


1.05 


59.99 


1.31 


59.98 


1.57 


59.97 


1.83 


60 
61 




60.99 


1.06 


60.99 


1.33 


60.98 


1.60 


60.97 


1.86 




6'i 


61.99 


1.08 


61.99 


1.35 


61.98 


1.62 


61.97 


1.89 


62 




63 


62.99 


1.10 


62.99 


1.37 


62.96 


1.65 


62.97 


1.92 


63 




64 


63.99 


1.12 


63.98 


1.40 


63.98 


1.68 


63.97 


1.96 


64 




65 


34.99 


1.13 


64.98 


1.42 


64.98 


1.70 


64.97 


1.99 


65 




66 


65.99 


1.15! 


65.98 


1.44 


65.98 


1.73 


65.97 


2.02 


66 




67 


66.99 


1.17. 


66.98 


1.46 


66.98 


1.75 


66.97 


2.05 


67 




68 


67.99 


1.19: 


67.98 


1.48 


67.98 


1.78 


67.97 


2.08 


68 




69 


68.99 


1.20 


68.98 


1.51 


68.98 


1.81 


68.97 


2.11 


69 




70 
71 


69.99 
70.99 


1.22 


69.93 


1.53 


39.98 


1.83 


69.97 


2.14 


70 




1.24 


70.98 


1.55 


70.98 


1.86 


70.97 


2.17 


71 




n 


71.99 


1.26 


71.98 


1.57 


71.98 


1.88 


71.97 


2.20 


72 




73 


72.99 


1.27 


72.98 


1.59 


72.97 


1.91 


72.97 


2.23 


7E 




74 


73.99 


1.29 


73.98 


1.61 


73.97 


1.94 


73.97 


2.26 


74 




75 


74.99 


1.31 


74.98 


1.64 


74.97 


1.96 


74.97 


2.29 


75 




76 


75.99 


1.33 


75.98 


1.66 


75.97 


1.99 


75.96 


2.32 


76 




77 


76.99 


1.34 


76.98 


1.68 


76.97 


2.02 


76.96 


2.35 


77 




7b 


77.99 


1.36 


77.98 


1.70 


77.97 


2.04 


77.96 


2.38 


78 




79 


78.9S 


1.38 


78.98 


1.72 


78.97 


2.07 


78.96 


2.41 


79 




SO 
81 


79.96 
80.99 


1.40 


79.98 


1.75 


79.97 


2.09 


79.96 


2.44 


80 




1.41 


80.98 


1.77 


80.97 


2.12 


90.96 


2.47 


81 




8:i 


81.96 


1.43 


81.98 


1.79 


81.97 


2.15 


81.96 


2.50 


82 




83 


82.99 


1.45 


82.98 


1.81 


82.97 


2.17 


82.96 


2.53 


83 




84 


83.99 


1.47 


83.98 


1.83 


83.97 


2.20 


63.96 


2.57 


84 




So 


84.98 


1.48 


84.98 


1.85 


84.97 


2.23 


84.96 


2.60 


85 




86 


85.96 


1.50 


85.98 


1.88 


85.97 


2.25 


85.96 


2.63 


86 




87 


86. 9£ 


1.52 


86.98 


1.90 


86.97 


2.28 


86.96 


2.66 


87 




88 


87.9S 


1.54 


87.98 


1.62 


87.97 


2,30 


87.96 


2.69 


88 




89 


88.96 


1.55 


88.98 


1.94 


38.97 


2.33 


88.96 


2.72 


89 




90 
91 


89.99 
90.96 


1.57 


89.98 


1.96 


89.97 


2.36 


89.96 


2.75 


90 
91 




1.59 


90.98 


1.99 


.90.97 


2.38 


90.96 


2.78 




92 


91.99 


1.61 


91.98 


2.01 


91.97 


2.41 


91.96 


2.8] 


92 




93 


■)2.96 


1.62 


92.98 


2.03 


92.97 


2.43 


92.96 


2.8' 


93 




94 


93.99 


1.64 


93.98 


2.05 


93.97 


2.46 


93.96 


2.87 


94 




95 


94.99 


1.66 


94.98 


2.07 


94.97 


2.49 


94.9fc 


2.9C 


95 




96 


95.99 


1.68 


95.98 


2.09 


95.97 


2.51 


95.9e 


2.9' 


96 




97 


96.96 


1.69 


96.98 


2.12 


96.97 


2.54 


96.9c 


2.96 


97 




98 


97.96 


1.71 


97.98 


2.14 


97.97 


2.57 


97.9c 


2.99 


9P 




99 


98.9t 


1.73 


98.98 


2.16 


98.97 


2.59 


98.9,= 


3.02 


9fl 




100 

5 


99.9t 


1.75 


99.98 


2.18 


99.9- 
Dep. 


2.62 


99.9c 
Dep 


3.0£ 


IOC 
en 




Dep 


Lat. 


Dep. 


Lat. 


Lat. 


Lat. 




89 Deg. 


88|Deg. 


1 88iDej?. 


SSiDeg 


a 





10 



42 



TRAVERSE TABLE. 



t 

00 

] 


J 2 Dog. 


2iDeg 


2iDeg 


1 ^^ ^^^- di 


Lat 


Dep. 

0.03 


Lat 


iDep 


Lat 


.IDep 


Lat 


. Dep. ."■ 


l.OC 


1.00 0.0< 


I i.ool 0.04II i.ool 0.05I ll 


2 


2.0C 


0.07 


2.00 O.Of 


2.0{ 


D 0.0£ 


2.00 0.10 2 


9 


3.0C 


O.IC 


3.00 0.12 


3.0( 


) 0.1£ 


3.00 0.14 3 


A 


4.0C 


0.1^ 


4.0f 


O.Ifi 


4.0( 


} o.r 


4.00 0.19 4 


£ 


5.0C 


0.17 


5.0C 


0.20 


5.0( 


) 0.22 


4.99 0.24 5 


6 


6.00 


0.2] 


6.0f 


0.24 


6.9S 


) 0.26 


5.95 


) 0.29 6 


7 


7.00 


0.24 


6.99 


0.27 


6.9J 


) 0.31 


6.9£ 


0.34 7 
0.38 8 
0,43 9 


8 


7.99 


0.28 


7.99 


0.3] 


7.9E 


0.35 


7.9£ 


. J) 


8.99 


0.31 


8.99 


0.35 


8.9E 


0.39 


8.9£ 


i(J 
11 


9.99 
10.99 


0.35 
0.38 


9.99 


0.39 


9.9£ 


0.44 


9.9£ 


0.48 10 


10.99 


0.43 


10.99 


0.48 


10.99 


0.53 11 


12 


11.99 


0.42 


11.99 


0.47 


11.99 


0.52 


11.99 


0.58 12 


la 


12.99 


0.45 


12.99 


0.51 


12.99 


0.57 


12.99 


0.62 13 


14 


13.99 


0.49 


13.99 


0.55 


13.99 


0.61 


13.98 


0.67 14 


15 


14.99 


0.52 


14.99 


0.59 


14.99 


0.65 


14.S8 


0.72 15 


16 


15.99 


0.56 


15.99 


0.63 


15.99 


0.70 


15.18 


0.77 16 


17 


16.99 


0.6S 


16.99 


0.67 


16.98 


0.74 


16.98 


0.82 17 


18 


17.99 


0.63 


17.99 


0.71 


17.98 


0.79 


17.98 


0.86 18 


19 


18.99 


0.66 


18.99 


0.75 


18.98 


0.83 


18.98 


0.91 19 
0.96 20 

1.01 21 


5>0 
21 


19.99 
20.99 


0.70 


19.98 


0.79 


19.98 
20.98 


0.87 


19.98 
20.98 


0.73 


20.98 


0.82 


0.92 


22 


21.99 


0.77 


21.98 


0.86 


21.98 


0.96 


21.97 


1.06 22 


23 


22.99 


0.80 


22.98 


0.90 


22.98 


1.00 


22.97 


1.10 23 


24 


23.99 


0.84 


23.98 


0.94 


23.98 


1.05 


23.97 


1.15 24 


25 


24.98 


0.87 


24.98 


0.98 


24.98 


1.09 


24.97 


1.20 25 


26 


25.98 


0.91 


25.98 


1.02 


25.98 


1.13 


-25.97 


1.25 28 


27 


26.98 


0.94 


26.98 


1.06 


26.97 


1.18 


26.97 


1.30 27 


28 


27.98 


0.98 


27.98 


1.10 


27.97 


1.22 


27.97 


1.34 28 


29 


28.98 


1.01 


28.98 


1.14 


28.97 


1.26 


28.97 


1.39 29 


30 
31 


29.98 
30.98 


1.05 


29.98 


1.18 

1.22 


29.97 
30.97 


1.31 


29.97 


1.44 30 
1.49 31 


1.08 


30.98 


1.35 


30.96 


32 


31.98 


1.12 


31.98 


1.26 


31.97 


1.40 


31.96 


1.54 32 


33 


32.98 


1.15 


32.97 


1.30 


32.97 


1.44 


32.96 


1.58 33 


34 33.98! 


1.19 


33.97 


1.33 


33.97 


1.48 


33.96 


1.63 34 


35 


34.98 


1.22 


34.97 


1.37 


34.97 


1.53 


3-4.96 


1.68 353 


36 


35.98 


1.26 


35.97 


1.41 


35.97 


1..57 


35.96 


1.73 36 


37 


36.98 


1.29 


36.97 


1.45 


36.96 


1.61 


36.96 


].7S 37 


38 


J7.98 


1.33 


37.97 


1.49 


37.96 


l.fifi 


37.96 


1.82 3S 


39 


38.98 


1.36 


38.97 


1.53 


38.96 


1.70 


38.96 


1.87 39 


40 
41 


39.98 


1.40 
1.43 


39.97 
40.97 


1.57 
1.61 


39.96 


1.75 

1.77 1 


39.95 
40.95 


1.92 40| 


40.98 


40.96 


1.97 4ll 


42 


41.97 


1.47 


41.97 


1.65 


41.96 


1.83 


41.95 


2.02 42I 


43 


42.97 


1.50 


42.97 


1.69 


42.96 


l.RS 


42.95 


2.06 43" 


44 


43.97 


1.54 


43.97 


1.73 


43.96 


1.92 


43.95 


2.11 44| 
2.16 455 


45 


44.97 


1.57 


44.97 


1.77 


44.96 


1.96 


44.95 


46 


45.97i 


1.61 


46.96 


1.81 


45.96 


2.01 


45.95 


2.21 46| 


47 


46.97 


1.64 


16.96 


1.85 


46.96 


2.05 


46.^5 


2.25 47| 
2.30 48'' 


48 


47.97 


1.6g 


47.96 


1.88 


17.95 


2.09 ■ 


47.96 


49 


48.97 


1.71 


48.96 


1.92 


48.95 


2.14 


18.94 


2.35 49, 
2.40 50 


50 
m 


49.97 


1.74 


49.96 


1.96 


49.95 


2.18 ' 


49,94 
Dep. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. ] 


Lat. ^• 


88 beg. 1 


87|Deg. 


B7iDeg. •< 


37iDeg.Q| 



TRAVERSE TABLE. 



5 

51 


2Deg. 


2iDeg 


2i Deg. 


21 Deg. 


o 

Cfi' 

51 


Lat. 


Dep. 


Lat. 


Dep. 

2.00 


Lat. 


Dep. 


Lat. 


Dep. 


50.97 


1.78 


50.96 


50.95 


2.22 


50.94 


2.46 


62 


51.97 


1.81 


51.96 


2.04 


51.95 


2.27 


51.94 


2.50 


52 


bS 


52.97 


1.85 


52.96 


2.08 


52.95 


2.31 


52.94 


2.. 54 


53 


54^53.97 


1.88 


53.96 


2.12 


53.95 


2.36 


53.94 


2. .59 


54 


55; 54. 97 


1.92 


54.96 


2.16 


54.95 


2.40 


54.94 


2.64 


56 


56 55.97 


1.96 


55.96 


2.20 


56.95 


2.44 


55.94 


2.69 


66 


57i56.97 


1.99 


56.96 


2.24 


56.95 


2.49 


56.93 


2.73 


67 


58;67.96 


2.02 


57.96 


2.28 


57.94 


2.53 


57.93 


2.78 


58 


59 58.96 


2.06 


58.95 


2.32 


58.94 


2.57 


58.93 


2.83 


59 


60 59.96 

61 60.96 


2.09 



2.13 


59.95 


2.36 


59.94 
60.94 


2.62 


59.93 


2.88 


60 


60.95 


2.39 


2.66 


60.93 


2.93 


61 


6261.96 


2.16 


61.95 


2.43 


61.94 


2.70 


61.93 


2.97 


62 


6362.96 


2.20 


62.95 


2.47 


62.94 


2.75 


62.93 


3.02 


63 


64 63.96 


2.23 


63.95 


2.51 


63.94 


2.79 


63.93 


3.07 


64 


65 64.96 


2.27 


64.95 


2.55 


64.94 


2.84 


64.93 


3.12 


66 


66 65.96 


2.30 


65.95 


2.59 


65.94 


2.88 


65.92 


3.17 


66 


8766.96 


2.34 


66.95 


2.63 


66.94 


2.92 


66.92 


3.21 


67 


6867.96 


2.37 


67.95 


2.67 


67.94 


2.97 


67.92 


3.26 


68 


69 


68.96 


2.41 


68.95 


2.71 


68.93 


3.01 


68.92 


3.31 


69 


70 
71 


69.96 


2.44 

2.48 


69.95 


2,75 


69.93 


3.05 


69.92 


3.36 


70 
71 


70.96 


70.95 


2.79 


70.93 


3.10 


70.92 


3.41 


72 


71.96 


2.51 


71.94 


2.83 


71.93 


3.14 


71.92 


3.45 


72 


73 


72.96 


2.55 


72.94 


2.87 


72.93 


3.18 


72.92 


3.50 


73 


74 


73.95 


2.58 


73.94 


2.91 


73.93 


3.23 


73.91 


3.55 


74 


75 


74.95 


2.62 


74.94 


2.94 


74.93 


3.27 


74.91 


3.60 


75 


76 


75.95 


2.65 


75.94 


2.98 


76.93 


3.31 


75.91 


3.65 


76 


77 


76.95 


2.68 


76.94 


3.02 


76.93 


3.36 


76.91 


3.70 


77 


78 


77.95 


2.72 


77.94 


3.06 


77.93 


3.40 


77.91 


3.74 


78 


79 


78.95 


2.76 


78.94 


3. in 


78.92 


3.45 


78.91 


3.79 


79 


80 
81 


79.95 


2.79 
2.83 


79.94 
80.94 


3.14 

3.18 


79.92 

80.92 


3.49 


79.91 


3.84 

3.89 


80 
81 


80.95 


3.53 


80.91 


82 81.95 


2.86 


81.94 


3.22 


81.92 


3.58 


81.91 


8.93 


82 


S3 


82.95 


2.90 


82.94 


3.26 


82.92 


3.62 


82.90 


3.98 


8.3 


84 


83.95 


2.93 


83.94 


3.30 


83.92 


3.66 


83.90 


4.03 


84 


85 


84.95 


2.97 


84.93 


3., 34 


84.92 


3.71 


84.90 


4.08 


85 


86 


85.95 


3.00 


85.93 


3.38 


35.9^ 


3.75 


85.90 


4.13 


S(i 


87 


86.95 


3.04 


86.93 


3.42 


80.92 


3.79 


86.90 


4.17 


87 


88 


87.95 


3.07 


87.93 


3.45 


87.92 


3.84 


87.90 


4.22 


88 


89 


88.95 


3.11 


88.93 


3.49 


88.92 


3.88 


88.90 


4.27 


89 


90 
91 


89.95 
90.95 


3.14 


89.93 


3.53 


89.91 


3.93 


89.90 


4.32 


90 
01 


3.18 


90.93 


3.57 


90.91 


3.97 


90.90 


4.37 


92 


91.94 


3.21 


91.93 


3.61 


91.91 


4.01 


91.89 


4.41 


92 


93 


92.94 


3.25 


92.93 


3.65 


92.91 


4.06 


92.89 


4.4C 


93 


94 


93.94 


3.28 


93.93 3.69 


93.91 


4.10 


93.89 


4.51 


94 


95 


94.94 


3.32 


94.93 3.73 


94.91 


4.14 


94.89 


4.5C 


95 


96 


95.94 


3.35 


95.93 3.77 


95.91 


4.19 


95.89 


4.61 


96 


97 


96.94 


3.39 


96.93 3.81 


96.91 


4.23 


96.89 


4.65 


97 


98 


97.94 


3.42 


97.92; 3.85 


97.91 


4.27 


97.89 


4.70 


98 


99 


98.94 


3.46 


98.92 3.89 


98.91 


4.32 


98.89 


4.75 


99 


100 
■*-» 

Q 


99.94 


3.49 


99.92^ 3.93 
Dep.] Lat. 


99.91 


4.36 


99.88 


4.80 


100 

to 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


88 De^. 


87fDe£. 


871 


Deg. 


87iDeg. 



44 



TRAVERSE TABLE. 



p. 

1 


3 Deg. II 31 Deg. 


H Deg. 


3fbeg. 




Lat. 


Dep. 


Lat. 
1.00 


Dep. 


Lat. Dep. 


Lat. 


Dep. 


1.00 


0.05 


0.06 


1.00 


0.06 


1.00 


0.06 


1 


2 


2.00 


0.10 


2.00 


0.11 


2.00 


0.12 


2.00 


0.13 


2 


3 


3.00 


0.16 


3.00 


0.17 


2.99 


0.18 


2.99 


0.20 


3 


4 


3.99 


0.21 


3.99 


0.23 


3.99 


0.24 


3.99 


0.26 


4 


5 


4.99 


0.26 


4.99 


0.28 


4.99 


0.31 


4.99 


0.33 


6 


6 


5.99 


0.31 


5.99 


0.34 


5.99 


0.37 


5.99 


0.39 


6 


7 


6.99 


0.37 


6.99 


0.40 


6.99 


0.43 


6.99 


0.46 


7 


8 


7.99 


0.42 


7.99 


0.45 


7.99 


0.49 


7.98 


0.52 


8 


9 


8.99 


0.47 


8.98 


0.51 


8.98 


0.56 


8.98 


0.69 


9 


10 


9.99 


0,52 


9.98 


0.67 


9.98 


0.61 
0.67 


9.98 


0.65 


10 
11 


11 


10.98 


0.58 


10.98 


0.62 


10.98 


10.98 


0.72 


12 


11.98 


0.63 


11.98 


0.68 


11.98 


0.73 


11.97 


0.78 


Is 


13 


12.98 


0.68 


12.98 


0.73 


12.98 


0.79 


12.97 


0.85 


13 


14 


13.98 


0.73 


13.98 


0.79 


13.97 


0.85 


13.97 


0.92 


14 


15 


14.98 


0.79 


14.98 


0.86 


14.97 


0.92 


14.97 


0.98 


15 


16 


15.98 


0.84 


15.97 


0.91 


15.97 


0.98 


15.97 


1.05 


16 


17 


16.98 


0.89 


16.97 


0.96 


16.97 


1.04 


16.96 


1.11 


17 


18 


17.98 


0.94 


1 17.97 


1.02 


17.97 


1.10 


17.96 


1.18 


18 


19 


18.98 


0.99 


18.97 


1.08 


18.96 


1.16 


18.96 


1.24 


19 


20 
21 


19.97 


1.05 


19.97 


1.13 


19.96 


1.22 


19.96 


1.31 


20 


20.97 


1.10 


20.97 


1.19 


20.96 


1.28 


20.96 


1.37 


21 


22 


21.97 


1.15 


21.96 


1.25 


21.96 


1.34 


21.96 


1.44 


22 


23 


22.97 


1.20 


22.96 


1.30 


22.96 


1.40 


22.95 


1.60 


23 


24 


23.97 


1.26 


23.96 


1.36 


23.96 


1.47 


23.95 


1.57 


24 


25 


24.97 


1.31 


24.96 


1.42 


24.95 


1.63 


24.95 


1.64 


25 


26 


25.96 


1.36 


25.96 


1.47 


25.95 


1.59 


25.94 


1.70 


26 


27 


26.86 


1-41 


26.96 


1.53 


26.95 


1.65 


26.94 


1.77 


27 


28 


27.96 


1.47 


r27.95 


1.69 


27.95 


1.71 


27.94 


1.83 


28 


29 


28.96 


1.52 


128.95 


1.64 


28.95 


1.77 


28.94 


1.90 


29 


30 
31 


29.96 
30.96 


1.57 


;29.95 

1 . . . 


1.70 


29.94 


1.83 


29.94 
30.93 


1.96 


30 
31 


1.62 


30.95 


1.76 


30.94 


1.89 


2.03 


32 


31.96 


1.67 


31.95 


1.81 


31.94 


1.96 


31.93 


2-09 


32 


33 


32.95 


1.73 


32.95 


1.87 


32.94 


2.01 


32.93 


2.16 


33 


34 


33.95 


1.78 


33.95 


1.93 


33.94 


2.08 


33.93 


2.22 


34 


35 


34.95 


1.83 


■34.94 


1.98 


34.93 


2.14 


34.92 


2.2£ 


35 


36 


35.95 


1.88 


35.94 


2.04 


35.93 


2.20 


35.92 


2.35 


36 


37 


36.95 


1.94 


36.94 


2.10 


36.93 


2.26 


36.92 


2.42 


37 


38 


37.95 


1.99 


37.94 


2.15 


37.93 


2.32 


37.92 


2.49 


38 


39 


38.95 


2.04 


38.94 


2.21 


38.93 


2.38 


38.92 


2.55 


39 


40 
41 


39.95 
40.94 


2.09 


39.94 
'40.93 


2.27 


39.93 


2.44 


39.91 


2.62 


40 
41 


2.15 


2.32 


40.92 


2.50 


40.91 


2.68 


42 


41.9^^ 


2.20 


41.93 


2.38 


41.92 


2.,56 


41.91 


2.75 


42 


43 


42.94 


2.25 


'42.93 


2.44 


42.92 


2.63 


42.91 


2.8] 


43 


44 


43.94 


2.30 


43.93 


2.49 


43.92 


2.69 


43.91 


2.88 


44 


45 


44.94 


2.36 


44.93 


2.55 


44.92 


2.75 


44.90 


2.9-3 


45 


46 


45.94 


2.41 


45.93 


2.61 


45.91 


2.81 


45.90 


3.01 


46 


47 


46.94 


2.46 


46.92 


2.66 


46.91 


2.87 


46.90 


3.07 


47 


48 


47.93 


2.51 


■47.92 


2.72 


47.91 


2.93 


47.90 


3.14 


48 


49 


48.93 


2.56 


48.92 


2.78 


48.91 


2.99 


48.90 


3.20 


49 


50 

CO 


49.93 


2.62 
Lat. 


^49.92 


2.83 


49.91| 3.05 
Dep. [Lat. 


49.89 


3.27 


50 


Dep. 


Dep. 


Lat. 


Dep. 


Lat. 




87 


Deg. 


;86f 


Deg. 


86iDeg. 


86lD€g. 



TRAVERSE TABLE. 




46 



TRAVERSE TABLE. 



5 


4Deg. 


H 


Deg. 


41 ■ 


Deg. 4| Deg. 


5 

CO 


03 

• 


Lat.lDep. 


Lat. 


Dep. Lat.JDep. i Lat. 


Dep. 


1 


I.OOJ 0.07 


1 l.OC 


0.07, i I.OOI 0.08 


1.00 0.03 


I 


2 


2.00i 0.14 


! 1.99 


0.15: 1.99 0.16 


1.99 0.17 





3 


2.99 


0.21 : 2.99 


0.221 2.99 0.24 


2.99 0.25 


S 


4 


3.99 


0.28 


3.99 


0.30 i 3.99 0.31 


3.98 0.33 


4 


5 


4.99 


0.35 


4.99 


0.37,: 4.98 0.39 


4.98 0.41 


5 


6 


5.99 


0.42 


5.98 


0.441 5.98 0.47 


5.98, 0.50 


6 


7 


6.98 


0.49 


6.98 


0.52i: 6.98: 0,55 


6.97 


0.58 


7 


8 


7.98 


0.56 


7.98 


0.59 


: 7.98 0.63 


7.97 


0.66 


8 


9 


8.98 


0.63 


8.98 


0.67 


1 8.97 0.71 


8.97 


0.75 


9 


10 


9.98 


0.70 
0.77 


9.97 


0.74 


9.97 0.78 


9.97 


0.83 


10 


111 10.97 


10.97 


0.82 


!l0.97 0.86 


10.96 


0.91 


11 


1211.97 


0.84 


11.97 


0.89 


'11.96 0.94 


11.96 


0.99 


12 


1312.97 


0.91 


12.96 


0.96 


|-12.96| 1.02 


12.96 


1.08 


13 


14l 13.97 


0.98 


13.96 


1.04 


!13.96! 1.10 


13.95 


1.16 


14 


15' 14.96 


1.05 


14.96 


1.11 


114.951 1.18 


14.95 


1.24 


15 


1615.96 


1.12 


15.96 


1.19|il5.95] 1.26 


15.95 


1.32 


16 


1716.96 


1.19 


16.95 


1.26! 16.951 1.33 


16.94 


1.41 


17 


18 17.96 


1.26117.95 


1.331:17.94 1.41 


17.94 


1.49 


16 


19;i8.95 


1.33,118.95 


1.40'; 18.94; 1.49 


18.93 


1.57 


19 


2019.95 
2l'20.95 


1.40''l9.95 

1 

1.46i 20.94 


1.481 19.94| 1.57 
1.56' 20.941 1.65 


19.93 


1.66 


20 


20.93 


1.74 


21 


2221.95 


1.53|21.94 


1.63' 21.93! 1-73 


(21.92 


1.82 


22 


2322.94 


1.60! 22.94 


1.70,22.93! 1.80 


;22.92 


1.90 


23 


24'23.94 


1.67li23.93 


1.78:!23.93 


1.88 


,23.92 


1.99 


24 


,25124.94 


1.74i,24.93 


1.85 24.92 


1.96 


24.91 


2.07! 25 


26 25.94 


1.81 25.93 


1.93125.92 


2.04 [25.91 


2.15; 26 


27 26.93 


1.88,1 i26.93 


2.00 26.92 


2.12 |26.91 


2.241 27 


2827.93 


1.951:27.92 


2.08 27.91 


2.20 127.90 


2.321 28 


29,28.93 


2.02! 128.92 


2. 15| 28.911 2.28! 128.90 


2.40; 29 


3029.93 2.09 


29.92 


2.22 29.91 2.35 


29.90 
30.89 


2.48 
2.57 


30 
31 


3ll30.92 2.16 


30.91 


2.30 30.90 2.43 


32 31.92 


2.23 


31.91 


2.37 31.901 2.51 


31.89 


2.65 


32 


33 32.92 


2.30 


32.91 


2.45, 32.90 2.59 32.89 


2.73 


33 


3433.92 


2.37 


33.91 


2.52; 33.90! 2.67 133.88 2.82 


34 


3534.91 


2.44 


34.90 


2.59; 34.89 2.75'i34.88 2.90J 35 


3635.91 


2.51 


35.90 


2.67 35.89 2.82:35.88 2.98 36 


37,36.91 


2.58 


36.90 


2.74 36.89 2.90;l36.67 3.06! ST 


38 37.91 


2.65 


37.90 


2.82 37.88 2.98, 


37.87 3.15! 38 


S9'38.90 2.72J 38.89 


2.89 38.88 3.06, 


38.87 3.231 39 


40.39.90 2.79 


39.89 
40.89 


2.96; 39.86 3.14 
3.04 40.87 3.22' 


39.86, 3.31 
40.86 3.40 


_4Q 
41 


4l|40.90 2.86 


42 41.90 2.93! 41.88 


3.1141.871 3.30 


41.86 3.48 


42 


43:42.90 3.00! 142.88 


3.19 42.87' 3.37 


42.85 3.56 


43 


4443.89 


3.071:43.88 


3.26 43.861 3.45 


43.85 


3.64 


44 


45:44.89 


3.14|!44.88 


3.33 44.86 3.53; 


44.85 


3.73 


45 


46 45.89 


3.2ll 45.87 


3.41 45.86 


S.61| 


45.84 


3.81 


45 


47 46.89 


3.28|i46.87 


3.48 46.86 


3.69; 


46.84 


3.89 


47 


48,47.88 


3.35 


47.87 


3.56 47.85 


3.77; 


47.84 


3.97 


48 


49,48.68 


3.42 


48.87 


3.63 43.85 


3.84 


48.83 


4.06 


49 


60 


49.68 


3.49 


49.86 


3.71J '49.85 


8.92 


49.83 


4.14 


50 


-s 
'^ 


Dep. 


Lat. 


Dep. 


Lat.JDep. 


Lat. 


Dep. 


Lat. 




86 Deg. 


86|DegJl85^Deg.l 


85iDeg.| 


-4 



TRAVERSE TABLE. 



4/ 



;-,; 4 Deg. j 4' Deg. 


4i Deg.jj 4J Deg. 


a 


r- Lat. 


Dep. Lat. 


Dep.' Lat. Dep. j 


Lat.jDep. 


5 
«-•• 


51 50.88 


3.56 50.86 


3.78 50.84 4.00/50.821 4.22 51 


52 51.87 


3.63 51.86 


3.85 51.84 4.08 i51.82; 4.31 52 


53 52.87 


3.70 52.85 


3.93 52.84 4.16 52.82! 4.39 53 


54 53.87 


3.77 53.85 


4.00 53.83 4.24 53.81i 4.47 54 


55 54.87 


3.84 54.85 


4.08 54.83 4.32I 54.811 4-55 55 


66 55.86 


3.91 55.85 


4.15 55.83 4.39 55.8II 4.64^ 56 


57 56.86 


3.98 56.84 


4.22 56.82 4.4?! 56.80 4.721 57 


58 57.86 


4.05 57.84 


4.30 57.82 4.55 57.80 4.80; 68 


59 58.86 


4.12158.84 


4.37 58.82 4.63 58.80; 4.89 


59 


6059.65 


4.19|59.84 


4.45 


59.82 4.71 |59.79i 4.97 
60.81 4.7916O.79: 5.05 


60 
61 


61 60.85 


4.26 60.83 


4.52 


62 61.85 


4.32 61.83 


4.59 61.81 4.86 61.79 5.13 62 


63 62.85 


4.39 62.83 


4.67 62.81! 4.94 62.78 5.22: 63 


64 63.84 


4.46 63.82 


4.74 63.80; 5.02 163.78 6.30 64 


65,64.84 


4.53 64.82 


4.82 64.80 5.10.64.78 5.38! 65 


66 65.84 


4.60 65.82 


4.89 65.80 5.18 165.77 5.47 66 


67 66.84 4.67 66.82 


4.97 66.79 5.26 66.77 6.55^ 67 


68 67.83^ 4,74 67.81 


5.04 


67.79 5.34 67.77 5.63 681 


69 68.83| 4.81 68.81 


5.11 


68.79i 5.41 68.76 5.71! 691 


70 69.831 4.88 69.81 


5.19 


j69.78 5.49 


69.76 5.80 70 


7170.83! 4.95 70.80 


5.26 


70.78 5.57 


!70.76 5.88 71 


72 71.82 5.02 71.80 


5.34 


71.78 5.65 


71.75 5.96 72 


73 72.82 5.09 72.80 


5.41 


72.77 5.73 


72.75 6.04 73 


74 73.82 5.16 73.80 


5.48 


73.77 5.81 


73.75 6.13 74 


75 74.82 5.23 74.79 


5.56 


74.77 5.88[ 74.74 6.21 75| 


76 75.81 5.30 75.79 


5.63 


75.77 5.96! 75.74 6.29 76| 


77 76.81 


5.37 76.79 


5.71 


76.76 6.04 


76.74 6.38 77 


78 77.81 


5.44 77.79 


5.781:77.76 6.12 


77.73 6.46 78 


79 78.81 


5.51 78.78 


5.85i78.76 6.20 


78.73 6.54 79 


80 79.81 
8180.80 


5.58 79.78 
5.65 80.78 


5.93 79.75 6.28 


79.73 6.62; 80 


6.00 80.75 6.36 


80.72' 6.71I 81 


82 81.80 


5.72 81.78 


6.08 81.75 6.43;!81.72 6.79- 82 


83 82.80 


5.79 82.77 


6.15i 82.74 6.51il82.71 6.87 83 


84 83.80 


5.86 83.77 


6.23i 83.74 6.59i|83.7i; 6.96 84 


85.84.79 


5.93 84.77 


6.30' 84.74 6.67 '84.71 7.04 85 


86'85.79 


6.00 85.76 


6.37| 85.73 6.75' 85.70 7.12 86 


8786.79 


6.07 86.76 


6.45 86.73 6.83 86.70 7.20 87 


88,87.79 


6.14 87.76 


6.52 87.73 6.90 87.70 7.29 88 


8988.78 


6.21 88.76 


6.60 88.73 6.98 88.70 7.37 89 


90,89.78; 6.23 89.75 

1 1 


6.67 89.72 7.06 


89.69 7.45 90 


9190.78 


6.35 90.75 6.74' 90.72 7.14 


90.69 7.54 91 


92 91.78 


6.42 91.75' 6.82 91.72 7.22! 91.68 7.62 921 


93 92.77 


6.49 92.741 6.89 92.71 7.3o! 92.68 7.70 93] 


94 93.77 


6.56 93.74 


6.97 93.71 7.38' 93.68 7.78 94 


95 94.77 


6.63.94.74 


7.04 94.71 7.45! 94.67 7.87 95 


96 95.77 


6.70 95.74 


7.11 95.70 7.53' 95.67 7.95 96 


97 96.76 


6.77 96.73 


7.19 96.70 7.6II 96.67 8.03 97 


98 97.76 


6.84 97.73 


7.26 97.70 7.69:97.66 8.12 98 


99*98.76 


6.91 98.73| 7.34 98.69 7.77' 98.66 8.20 99| 


100199.76 


6.98 99.73 7.41 99.69 7.85 


99.66 8.28 100 


^ JDep. 

•XI 


Lat. [pep. Lat.j'Dep. Lat. 


JDep.; Lat. ^ 

\ ■ ^ 


Ql 86 


Deg.ii863Deg.'85]Deg. 


laSiDeg. 


Qj 



48 



TRAVERSE TABLE. 



2i 


5 Deg. 


5i beg.i 


5i Deg. 1 6;^ Deg. 




»-<• 


Gf3 . ^ ' 'l 

r* Lat. Dep. 1 


Lat. Dep. Lat.l 


Dep. ; Lat. 


Dep. 


00 


1 1.00 


0.091 1.00 0.09 1.00 


0.10 0.99 


0.10 


~1 


2 1.99 


0.17! 1.99 0.18 1.99 


0.19 1.99 


0.20 


2 


3 2.99 


0.26 2.99 0.27 2.99 


0.29 2.98 


0.30 


3 


4 3.98 


0.36 ! 3.98 0.37 3.98 


0.38 3.98 


0.40 


4 


5 4.98 


0.44 j 4.98 0.46 4.98 


0.48 4.97 


0.50 


5 


6 5.98 


0.52' 5.97 0.55 5.97 


0.58 5.97 


0.60 


6 


7 6.97 


0.61 6.97 0.64 6.97 


0.67 6.96 


0.70 


7 


a; 7.97 


0.70 7.97 0.73 7.96 


0.76 7.96 


0.80 


8 


9 8.97] 


0.78 8.96 0.82^ 8.96 


0.86 8.95 


0.90 


9 


10| 9.96 

1 1 


0.87 9.96 0.92 


9.95 


0.96 9.95 


1.00 


10 


ll!l0.96| 0.96 


10.95 J.Ol 


10.95 


1.05 10.94 


1.10 11 


1211.95 1.05 


11.95 1.10 11.94 


1.16 11.94 


1.20 12 


1312.95 1.13 


12.95: 1.19 12.94 


1.25| 12.93 


1,30 13 


1413.95 1.22 


13.94, 1.28 13.94 


1.34 13.93 


1.40 14 


15 14.941 1.31 


14.94; 1.37 14.93 


1.44 14.92 


1.60 15 


16 15.94; 1.39 


16.93 1.46 16.93 


1.53 15.92 


1.60 16 


1716.94] 1.48 


16.93 1.56 16.92 


1.63 16.91 


1.70 17 


1817.93 1.57 


17.92; 1.65! 17.92 


1.73 17.91 


1.80 18 


19 18.93 1.66 


18.92; 1.74 18.91 


1.82 18.90 


1.90 19 


20,19.92 1.74 


19.92i 1.83 


19.91 


1.92 19.90 


2.00, 20 


2120.92 1.83 


20.91 1.92 


20.90 


2.01 20.89 


2.10 21 


22 21.921 1.92 


21.911 2.01 


21.90 


2.11i 21.89 


2,201 22 


2322.91 2.00 


22.90 2.10 


22.89 


2.20: 22.88 


2.30' 23 


2423.91 2.09 


23.90 2.20 


23.89 


2.301 23.88 


2.401 ^ 


35 24.90 2.18 


24.90 2.29 


24.88 


2.401 24.87 


2.50 25 


26 25.90 2.27 125.89: 2.38 


25.88 


2.49; 26.87 


2.60! 26 


27 26.90 2.35 126.89^ 2.47 


26.88 


2.59 26.86 


2.71 


27 


28 27.89 2.44 27.88; 2.56 


27.87 


2.68 27.86 


2.81 


28 


29 28.89 2.53 28.88; 2.65 


28.87 


2.78; 28.86 


2.91 


29 
30 


30;29.89 2.6i; 29.87; 2.75 


29.86 


2.88| 29.85 


3.01 


31'30.88 2.70'30.87 2.84 








! 


30.86 


2.97 30.84 


3.11; 3l| 


32;31.83 2.79:i31.87i 2.93 


31.85 


3.07: 31.84 


3.21 


32 


33^32.87 2.88 132.86! 3.02 32.85 


3.16132.83 


3.31 


33 


34^33.87 2.96 


33.86; 3.11 33.84 


3.26 33.83 


3.41 


34 


35!34.87 3.05 


34.86; 3.20 34.84 


3.35 


34.82 


3.51 


35 


36'35.86 3.14 


35.85: 3.29 35.83 


3.45 


35.82 


3.61 


36 


37136.86 3.22 


36.841 3.39 36.83 


3.55 


36.81 


3.71 


37 


38'37.86 3.31 


37.84; 3.48 37.83 


3.64 37.81 


3.81 


3S 


39J38.85 3.40 


38.841 3.57 38.82 


3.74 38.8C 


3.91 


39 
40 


4039.85' 3.49 


39.831 3.66 


39.82 


3.83 


39.80 


4.01 


41 40.84 3.57 40.83J 3,75 


40.81 


3.93 


40.79 


4.11 


41 


42'41.84i 3.66 41.82| 3.84 41.81 


4.031 41.79 


4.21 


42 


43;42.84i 3.75:142.82 


3.93 42.80 


4.12 


;42.7g 


4.31 


43 


44:43.83 


3.83i:43.82 


4.03 43.80 


4.22 


'43.78 


4.41 


44 


45 44.83 


3.92'i44.81 


4.12 44.79 


4.31 


44.77 


4.51 


45 


46'45.82 


4.01ij45.81 


4.21 45.79' 4.41 


:45.77 


4.61 


46 


47 46.82 


4.10146.80 


4.30 46.781 4.50 


46.76 


4.71 


47 


48|47.82 


4.18|47.80 


4.39 '47.78 


4.60 


47.76 


4.81 


43- 


49148.81 


4.271,48.79 


4.48:48.77 


4.70 


146.75 


4,91 


49 


50 


49.81 


4.36 


49.79 
Dep. 


4.58 


49.77 


4.79 


J49.75 


6.01 
Lat. 


50 

CO 




Dep. 


Lat. 


Lat. 


Dep. 


Lat. 


Dep. 


85 Deg. 


843 


Peg. 


84iDeg. 


84iDeg. 



TRAVERSE TABLE. 



49 



51 


5Deg. 


5iDeg. 


H Deg. 


5 J Deg. 


5 

CO 

51 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


50.81 


4.44 


50.79 


4.67 


50.77 


4v89 


50.74 


5.11 


52 


51.80 


4.53 


51.78 


4.76 


51.76 


4.98 


51.74 


5.21 


52 


53 


52.8C 


4.62 


52.78 


4.85 


52.76 


5.08 


52.73 


5.31 


5S 


54 


53.79 


4.71 


53.77 


4.94 


53.75 


5.18 


53.73 


,5.41 


54 


55 


54.79 


4.79 


54.77 


5.03 


54.75 


5.27 


54.72 


6.51 


55 


56 


55.79 


4.88 


55.77 


5.12 


55.74 


5.37 


55,72 


5.61 


56 


57 


56.78 


4.97 


56.76 


5.22 


56.74 


5.46 


56.71 


6.71 


57 


58 


57.78 


5.06 


57.76 


5.31 


57.73 


5.56 


57.71 


5.81 


58 


59 


58.78 


5.14 


58.75 


5.40 


58.73 


5.65 


58.70 


5.91 


59 


60 
61 


59.77 


5.23 


59.75 


5.49 


59.72 


5.75 
5.85 


59.70 6.01 
60.69 6.11 


60 
61 


60.77 


5.32 


60.74 


5.58 


60.72 


62 


61.76 


5.40 


61.74 


5.67 


61.71 


5.94 


61.69! 6.21 


62 


63 


62.76 


5.49 


62.74 


5.76 


62.71 


6.04 


62.68| 6.31 


63 


64i63.76 


5.58 


63.73 


5.86 


63.71 


6.13 


63.68 6.41 


64 


65 1 64. 75 


5.67 


64.73 


5.95 


64.70 


6.23 


64.67 6.51 


65 


66 


65.75 


5.75 


65.72 


6.04 


65.70 


6.33 


65.67 6.61 


66 


67 


66.75 


5.84 


66.72 


6.13 


66.69 


6.42 


66.66 


6.71 


67 


68 


67.74 


5.93 


67.71 


6.22 


67.69 


6.52 


67.66 


6.81 


68 


69 


68.74 


6.01 


68.71 


6.31 


68.68 


6.61 


68.65 


6.91 


69 


70 
•71 


69.73 


6.10 


69.71 


6.41 


69.68 
70.67 


6.71 


69.65 


7.01 


70 


70.73 


6.19 


70.70 


6.50 


6.81 


70.64 


7.11 


71 


72 


71.73 


6.28 


71.70 


6.59 


71.67 


6.90 


71.64 


7.21 


72 


73 


72.72 


6.36 


72.69 


6.68 


72.66 


7.00 


72.63 


7.31 


73 


74 


73.72 


6.45 


73.69 


6.77 


73.66 


7.09 


73.63 


7.41 


74 


75 


74.71 


6.54 


7469 


6.86 


74.65 


7.19 


74.62 


7.51 


75 


76 


75.71 


6.62 


75.68 


6.95 


75.65 


7.28 


75.62| 7.61 


76 


77 


76.71 


6.71 


76.68 


7.05 


76.65 


7.38 


76.61 7.71 


77 


78 


77.70 


6.80 


77.67 


7.14 


77.64 


7.48 


77.61 7.81 


78 


79 


78.70 


6.89 


78.67 


7.23 


78.64 


7.57 


78.60 7.91 


79 


80 
81 


79.70 


6.97 
7.06 


79.66 


7.32 


79.63 
80.63 


7.67 


79.60 a02 


80 


80.69 


80.66 


7.41 


7-76 


80.59| 8.12 


81 


82 


81.69 


7.15 


81.66 


7.50 


81.62 


7.86 


81.59 8.22 


82 


83 


82.68 


7.23 


82.65 


7.59 


82.62 


7.96 


82.581 8.32 


83 


84 


83.68 


7.32 


83.65 


7.69 


83.61 


8.05 


83.58 8.42 


84 


85 


84.68 


7.41 


84.64 


7.78 


84.61 


8.15 


84.57 8.52 


85 


86 


8.5.67 


7.50 


85.64 


7.87 


85.60 


8.24 


85.57 8.62 


86 


87 


86.67 


7.58 


86.64 


7.96 


86.60 


8.34 


86.56 


8.72 


87 


88 


87.67 


7.67 


87.63 


8.05 


87.59 


8.43 


87.56 


R.S2 


88 


89 


88.66 


7.76 


88.63 


8.14 


88.59 


8.53 


88.55 


8.92 


89 


90 
91 


89.66 


7.84 


89.62 


8.24 


89. 5t! 


8.63 


89.55 


9,02 


90 


90.65 


7.93 


90.62 


8.33 


90.58 


8.72 


90.54' 9.12 


91 


92 


91.65 


8.02 


91.61 


8.42 


91.58 


8.82 


91.54] 9.22 


92 


93 


92.65 


8.11 


92.61 


8.51 


92.57 


8.91! 


92.53 9.32 


93 


94 


93.64 


8.19 


93.61 


8.60 


93.57 


9.011 


93.53! 9.42 


94 


95 


94.64 


8.28 


94.60 


8.69 


94.56 


9.11) 


94.52 9.52 


95 


96 


95.63 


8.37 


95.60 


8.78 


95.56 


9.20 


95.52 9.62 


96 


97 


96.63 


8.45 


96.59 


8.88 


96.55 


9.30 


96.51! 9.72 


97 


98 


97.63 


8.54 


97.59 


8.97 


97.55 


9.39 


97.51 9.82 


98 


99 


98.62 


8.63 


98.59 


9.06 


98.54 


9.49' 


98.50 9.92 99 


100 


99.62 


8.72 


99.58 


9.15 


99.54 


9.58 

1 

Lat.l 

1 


99.50 10.02 100 


CO 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Dep.| Lat. 


cc 


Q 


85 Deg.l 


84fbeg.| 


84iDeg.| 


841 Deg. 


Q 



12 



50 



TRAVERSE TABLE. 



o 

CO 


6Deg. 


61 Deg. 


6i Deg. 


6^ Deg. 


9 

CO 


Lat. 


Dep. 


Lat. Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.99 


0.10 


0.99 0.11 


0.99 


0.11 


0.99 


0.12 


1 


2 


1.99 


0.21 


1.99 0.22 


1.99 


0.23 


1.99 


0.24 


2 


3 


2.98 


0.31 


2.98i 0.33 


2.98 


0.34 


2.98 


0.35 


3 


4 


3.98 


0.41 


3.981 0.44 


3.97 


0.45 


3.97 


0.47 


4 


S 


4.97 


0.52 


4.97| 0.54 


4.97 


0.57 


4.97 


0.59 


5 


6 


5.97 


0.63 


5.96i 0.65 


5.96 


0.68 


5.96 


0.71 


6 


7 


6.96 


0.73: 


6.961 0.76 


6.96 


0.79 


6.95 


0.82 


7 


R 


7.96 


0.84 


7.95: 0.87 


7.95 


0.91 


7.94 


0.94 


8 


9 


8.95 


0.94 


8.95 


0.98 


8.94 


1.02 


8.94 


1.06 


9 


10 
11 


9.95 


1.05 


9.94 


1.09 


9.94 


1.13 


9.93 


1.18 


10 
11 


10.94 


1.15 


10.93 


1.20 


10.93 


1.25 


10.92 


1.29 


12 


11.93 


1.25' 


11.93 


1.31 


11.92 


1.36 


11.92 


1.41 


12 


13 


12.93 


1.36] 


12.92 


1,42 


12.92 


1.47 


12.91 


1.53 


13 


14 


13.92 


1.46' 


13.92 


1.52 


13.91 


1.59 


13.90 


1.65 


14 


15 


14.92 


1.57 


14.91 


1.63 


14.90 


1.70 


14.90 


1.76 


15 


16 


15.91 


1.67 


15.90 


1.74 


15.90 


1.81 


15.89 


1.88 


16 


17 


16.91 


1.78 


16.90 


1.85 


16.89 


1.92 


16.88 


2.00 


17 


1ft 


17.90 


1.88 


17.89 


1.96 


17.88 


2.04 


17.88 


2.12 


18 


19 


18.90 


1.99 


18.89 


2.07 


18.88 


2.15 


18.87 


2.23 


19 


20 19.89 

21 20.88 


2.09 


19.88 


2.18 


19.87 


2.26 


19.86 


2.35 


20 
21 


2.20 


20.88 


2.29 


20.87 


2.38 


20.85 


2.47 


22 21.88 


2.30 


21.87 


2.40 


21.86 


2.49 


21.85 


2.59 


22 


23 22.87 


2.40 


22.86 


2.50 


22.85 


2.60 


22.84 


2.70 


23 


24 


23.87 


2.51 


23.86 


2.61 


23.85 


2.72 


23.83 


2.82 


24 


25 


24.86 


2.61 '24.851 2.72 


24.84 


2.83 


24.83 


2.94 


25 


26 


25.86 


2.72i25.85i 2.83 


25.83 


2.94 


25.82 


3.06 


26 


27 


26.85 


2.82 


26.84, 2.941 126.83 


3-06 


26.81 


3.17 


27 


28 


27.85 


2.93 


27.83 


3.05: '27.82 


3.17 


27.81 


3.29 


28 


29 


28.84 


3.03 


28.83 


3.16 |28.81 


3.28 


28.80 


3.41 


29 


30 
31 


29.84 


3.14 


29.82 


3.27 '29.81 


3.40 


29.79 


3.53 


30 

■ 

31 


30.83 


3.24! {30.82 


3.37! '30.80 


3.51 


30.79 


3.64 


32 


31.82 


3.3431.81; 3.48131.79 


3.62 


31.78 


3.76 


32 


33 


32.82 


3.45|!32.80: 3.59 32.79 


3.74 


32.77 


3.88 


33 


34 


33.81 


3.55' 33.80 3.70,33.78 


3.85 


33.76 


4.00 


34 


35 


34.81 


3.66i34.79| 3.8l| 34.78 


3.96 


34.76 


4.11 


35 


36 


35. 8C 


3.76 35.79 3.92 


135.77 


4.08 


35.75 


4.23 


36 


37 


36. 8C 


3.87 36.78 4.03 


136.76 


4.19 


36.75 


4.35 


37 


38 


37.79 


3.97 37.77 4.14 


37.76 


4.30 


37.74 


4.47 


38 


39 


38.79 


4.08 38.771 4.25 


38.75 


4.41 


38.73 


4.58 


39 


40 


39.78 


4.18 39.76J 4.35 


139.74 


4.53 


39.72 

■40.72 


4.70 


40 
41 


41 


40.78 


4.29 140.76; 4.46; 40.74 


4.64 


4.82 


42 


41.77 


4.39 i41.75! 4.57! 41.73 


4.76 


41.71 


4.94 


4<3 


43 


42.76 


4.49 42.74! 4.681 42.72 


4.87 


42.70 


5.05 


43 


44 


43.76 


4.60i43.74 4.79,43.72 


4.98 


43.70 


5.17 


41 


45 


44.75 


4.70i44.73' 4.90; 44.71 


5.09 


44.89 


5.29 


45 


4b 


45.75 


4.81 


45.73; 5.011:45.70 


5.21 


45.68 


5.41 


46 


47l46.7< 


4.91 


46.72! 5.12 


i46.7(J 


5.32 


46.67 


5.52 


47 


48 


47.74 


5.02 


!47.7i: 5.25 


,47.69 


6.43 


147.67 


5.64 


48 


4i) 


48. 7J 


.5.12 


48.71: 5.3^ 


48.69 


5.55 


;48.66 


6.76 


49 


SL 


49.73 


5.2.S 


49.70! 6.44 


49.68 


5.66 


49.65 


5.88 


50 


<-> 

CO 

Q 






1 

Dep.i Lat. 










4-J 

CO 


Dep 


Lat 


Dep. 


Lat. 


Dep, 


Lat. 


84 Deg. 


IsSfDeg. 


83iDeg 


SSiDeg. 



TRAVERSE TABLE. 



51 



P. 


6Deg. 


6i Deg. 


6 i Deg. 


6iDeg. 


o 

«-t- 


51 


Lat. 


Dep. 


Lat. Dep. 
60.70 5.55 


Lat. 


Dep. 


Lat. 


Dep. 


50.72 


5.33 


50.67 


5.77 


50.65 


5.99 


51 


52 


51.72 


5.44 


51.69 5.66 


51.67 


5.89 


51.64 


6.111 52 


53 


52.71 


5.54 


52.68 5.77 


52.66 


6.00 


52.63 


6.23 53 


54 


53.70 


5.64 


53.68 5.88 


53.65 


6.11 


53.63 


6.35 54 


55 


54.70 


5.75 


54.67 5.99 


54.65 


6.23 


54.62 


6.46 55 


56 


55.69 


5.85 


55.67 6.10 


55.64 


6.34 


55.61 


6.58J 56 


57 


56.69 


5.96 


56.66 6.21 


56.63 


6.45 


56.60 


6.70 57 


58 


57.68 


6.06 


57.66 6.31 


57.63 


6.57 


57.60 


6.82' 58 


59 


58.68 


6.17 


58.65 6.42 


58.62 


6.68 


58.59 


6.93 59 


60 


59.67 


6.27 


59.64 6.53 
60.64 6.64 


59.61 


6.79 


59.58 


7.05! 60 


61 


60.67 


6.38 


60.61 


6.91 


60.58 


7.17 61 


62 


61.66 


6.48 


61.63 6.75 


61.60 


7.02 


61.57 


7.29! 62 


63 


62.65 


6.59 


62.63 6.Sb 


62.60 


7.13 


62.56 


7.40 63 


64 


63.65 


6.69 


63.62' 6.97 


63.59 


7.25 


63.56 


7.52 64 


65 


64.64 


6.79 


64.61 7.08 


64.58 


7.36 


64.55 


7.64 65 


66 


65.64 


6.90 


65.61 7.19 


65.58 


7.47 


65.54 


7.76 66 


67 


66.63 


7.00 


66-60 7.29 


66.57 


7.58 


66.54 


7.88 67 


68 


67.63 


7.11 


67.60 7.40 


J67.55 


7.70 


67.53 


7.99 68 


69 


68.62 


7.21 


68.59 7.51 


68.56 


7.81 


68.52 


8.11 69 


70 
71 


69.62 


7.32 


69.58 7.62 
70.58: 7.73 


69.55 
70.54 


7.92 


69.51 


8.23 70 
8.35 71 


70.61 


7.42 


8.04 


70.51 


72 


71.61 


7.53 


71.57, 7.84 


71.54 


8.15 


71.50 


8.46 72 


73 


72.60 


7.63 


72.57, 7.95 


72.53 


8.26 


72.49 


8.58 73 


74 


73.59 


7.74 


73.56! 8.06 


73.52 


8.38 


73.49 


8.70 74 


75 


74.59 


7.84!j74.55i 8.17 


74.52 


8.49 


74.48 


8.82, 75 


76 


75.58 


7.94;j75.55' 8.27 


75.51 


8.60 


75.47 


8.93 76 


77 


76.58 


8.05 176.54' 8.38 


76.5! 


8.72 


76.47 


9.05 77 


78 


77.57 


6.15 


177.54 8.49 


77.50 


8.83 


77.46 


9.17 78 


79 


78.57 


8.26 


78.53 8.60 


78.49 


8.94 


78.45 


9.29 79 


80 
81 


79.56 


8.36 


79.53! 8.71 
80.52: 8.82 


79.49 


9.06 


79.45 


9.40 80 


80.56 


8.47 


80.46 


9.17 


80.44 


9.52 81 


82 


81.55 


8.57 


81.51 8.93 


81.47 


9.28 


81.43 


9.64 82 


83 


82.55 


8.68 


82.51 9.04 


82.47 


9.40 


82.42 


9.76 83 


84 


83.54 


8.78i83.50; 9.14 


83.46 


9.51 


83.42 


9.87 84 


85 


84.53 


8.88 184.50 9.25 


84.45 


9.62 


84.41 


9.99 85 


86 


85.53 


8.99 85.49 9.36 


85.45 


9.74 


85.4C 


10.11 86 


87 


86.52 


9.09! 86.48: 9.47 


86.44 


9.85 


86. 4C 


10.23 87 


88 


87.52 


9.20J 87.48 9.58 


87.43 


9.96 


87.3S 


10.34 88 


89 


88.51 


9.30i 88.47 9.69 


88.43 


10.08 


88.3S 


10.46 89 


90 
91 


89.51 


9.41 89.47j 9.80 
9.51 90.46 9.91 


89.42 


10.19 


89.38 


10.58 90 
10.70 91 


90.50 


90.42 


10.30 


90.3- 


92 


91.50 


9.62^91.45 10.02 


91.41 


10.41 


91.36 


10.81, 92 


93 


92.49 


9.72 92.45 10.12 


92.40 


10.53 


92.36 


10.93 93 


94 


93.49 


9.83' 93.44 10.23 


93.40 


10.64 


93.35 


11.05 94 


95 


94.48 


9.931 94.^14 10.34 


94.39 


10.75 


94.34 


11.17 95 


96 


95.47 


10.03|!95.43 10.45 


95.38 


10.87 


95.33 


11.28) 96 


97 


96.47 


10.14 


96.42 10.56 


96.38 


10.98 


96.33 


11.40 97 


98 


97.46 


10.24 


97.42 10.67 


97.37 


11.09 


97.32 


11.52'' 98 


99 


98.46 


10.35 


98.4110.78 


98.36 


11.21 


98.31 


11.64 98 


100 


99.45 


10.45 


99.41110.89 


99.36 


11.32 


99.31 


11.75|100 


• 


Dep. 


Lat. 


Dep. Lat. 


Dep. 


Lat. 


Dep. 


Lat 


\i 


84 Deg. 


SS^Deg. 


83iDeg. 


83iDeg. 


t 



i>2 



TRAVERSE TABLE. 





o 


7 Deg. 


'J\ Deg. 


7i Deg. 


7J Deg. 


C 




p. 


Lat. 


Dep. 


Lat.JDep. 


Lat, 


Dep, 


Lat. 


Dep. 






1 


0.99 


0.12 


0.99| 0.13 


0.99 


0.13 


0.99 


0.13 1 




2 


1.99 


0.24 


1.98! 0.25 


1.98' 0.26 


1.98 


0.27 2 




3 


2.98 


0.37 


2.98 0.38 


2.97 0.39 


3.97 


0.40 3 




4 


3,97 


0.49 


3.97 0.50 


3.97 0.52 


3.96 


0.54 


4 




5 


4.96 


0.61 


4.96 0.63 


4.96 0.65 


4.95 


0.67 


S 




6 


5.96 


0.73 


5.95 0.76 


5.95 0.78 


5.95 


0.81 


6 




7 


6.95 


0.85 


6.94 0.88 


6.94 0.91 


6.94 


0.94 


7 


j 


8 


7.94 


0.97 


7.94 1.01 


7.93 1.04 


7.93 


1.08 


8 


9 


8.93 


1.10 


8.931 1.14 


8.92 1.17 


8.92 


1.21 


9 




10 


9.93 


1.22 


9.92 1.26 
10.91 1.39 


9.91 


1.31 


9.91 


1.35 


10 
11 




11 


10.92 


1.34 


10.91 


1.44 


10.90 


1.48 




12 


11.91 


1.46 


11.90 1.51 


11.90 


1.57 


11.89 


1.62 


12 




13 


12.90 


1.58 


12.90 1.64 


12.89 


1.70 


12.88 


1.75 


13 




14 


13.90 


1.71 


13,89 1.77 


13.88 


1.83 


13.87 


1.89 


14 




15 


14.89 


1.83 


14.88 1.89 


14.87 


1.96 


14.86 


2.02 


15 




16 


15.88 


1.95 


15.87 2.02 


15.86 


2.09 


15.85 


2.16 


16 




17 


16.87 


2.07 


16.86 2.15 


16.85 


2.22 


16.84 


2.29 


17 




18 


17.87 


2.19 


17.86 2.27 


17.85 


2.35 


17.84 


2.43 


18 




19 


18.86 


2.32 


18.85 2.40 


18.841 2.481 


18.83 


2.56 


19 




20 
21 


19.85 


2.44 
2.56 


19.84 2.52 


19.83 


2.61 


19.82 


2.70 


20 
21 




20.84 


20.83 2.65 


20.82 


2.74 


20.81 


2.83 




22 


21.84 


2.68 


21.82 2.78 


21.81 


2.87 


21.801 2.97 


22 




23 


22.83 


2.80 


22,82 2.90 


22.80! 3.00 


22.79 3.10 


23 




24 


23,82 


2.92 


23.81 3.03 


23.79' 3.13 


23.78' 3.24 


24 




25 


24.81 


3.05 


24.80 3.15 


24.79; 3.26 


24.77 3.37 


25 




26 


25.81 


3.17 


25.79 3.28 


25.781 3.39 


25.76 3.51 


26 




27 


26.80 


3.29 


26.78 3.41 


26.77 


3.52 


26.75 3.64 


27 




28 


27.79 


3.41 


27.78 3.53 


27.76 


3.65 


27.74 


3.78 


28 




29 


28.78 


3.53 


28.77 3.66 


28.75 


3-.79 


28.74 


3.91 


2S 




30 
31 


29.78 


3.66 


29.76 3.79 
30.75 3.91 


29.74 


3.92 
4.05 


29.73 


4.05 


30 
31 




30.77 


3.78 


30.73 


30,72 


4.18 




32 


31.76 


3.90 


31.74 4.04 


31.73 


4.18 


.?1.71 


4,32 


32 




33 


32.75 


4.02 


32.74 4.16 


32.72 


4.31 


32.70 


4.45 


33 




34 


33.75 


4.14 


33.73 4.29 


33.71 


4.44 


33.691 4.58 


34 




35 


34.74 


4.27 


34.72 4.42 


134.70' 4.57 


34.68: 4.72 


35 




36 


35.73 


4.39 


35.71 4.54 


|35.69 4.70 


35.67' 4.85 


36 




37 


36.72 


4.51 


36.70 4.67 


i36.68 4.83 


36.66; 4.99 


37 




38 


37.72 


4.63 


37.70; 4.80 


i37.67 4.96 


37.65i 6.12 


38 




39 


38.71 


4.75 


38.69i 4.92 


38.67 6.G9 


38.64 


6.26 


39 




40 


39.70 


4.87 


39.68 5.05 
40.67 5.17 


39.66 5.22 
40.65 6.35 


39.63 


5.39 


40 
41 




41 


40.70 


5.00 


40.63 


5.53 




42 


41.69 


5.12 


41.66 6.30 


|41.64| 5.48 


41.621 5.66 


42 




43 


42.68 


5.24 


42.661 6.43 


142.63 6.61 


42.61! 5.80 


43 




44 


43.67 


6.36 


43.65' 5.55 


43.62 5.74 


43.60 5.93i 44 




45 44.67 


5.48 


44.64 5.68 


44.62; 5.87 


44.59' 6.07| 45 
45.58 6.201 46 




46:45.66 


5.61 


45.63 6.81 


45.61; 6.00 




4746.66 


5.73 


46.62 5.93 


46.60' 6.13 


46.57 6.34; 47 




48147.64 


5.85 


47.62 6.06 


47.59; 6.27 


47.56; 6.47 


48 




49 


48.63 


5.97 


48.61 6.18 


48,58i 6.40 


48.55; 6.61 


49 




60 


49.63 


6.09 


49.60| 6.31 


49.57! 6.53 


49.54| 6.74 


50 




3 


Dep. 


Lat. 


Dep.l Lat. 


Dep.' Lat. 


Dep.l Lat. 


00 




83 Deg. 


l823Deg. 


821 


Deg. 


82il 


Peg. 


5 



TRAVERSE TABLE 




51 50.62 

52 51.61 

53 52.60 

54 53.60 

55 54.59 

56 55.58 

57 66.58 

58 57.67 

59 58.56 

60 59.55 

61 60.65 

62 61.54 

63 62.63 

64 63.52 

65 64.52 

66 65.51 

67 66.60 

68 67.49 

69 68.49 
7069.48 

71 70.47 

72 71.46 

73 72.46 

74 73.45 

75 74.44 

76 75.43 

77 76.43 

78 77.42 

79 78.41 

80 79.40 



.43 160.51 
.56 161.50 

.68 [62.50 
.80 J63.49 
.92; 64.48 
.04: 65.47 
.17166.46 
.29j 67.46 
.41 1 68.45 
.53169.44 



7060.48 7.96 

82 61.47 8.09 

95 62.46 8.22 

08 63.45 8.35 

20|64.44 8.48 

33 165.44 8.61 

46 166.43 8.75 



60.44i 8 

61.43 8 

62.42: 8 

63.42 8 

64.41 8 

65.40 8 

66.39i 9 

67.38. 9 

68.37 9 

69.36! 9 




9190.32 11.09 
9291.31 11.21 

93 92.81 11.35 

94 93.3011.46 

95 94.29 11.58 

96 95.28 11.70 

97 96.28 11.82 

98 97.27 11.94 

99 98.2612.07 
100 99.2512.19 



90.27 
91.26 
92.26 
93.25 
94.24 



11.48 
11.61 
11.74 
11.86 
11.99 



95.23112.12 
96.22112.24 
97.22112.37 
98.21 12.49 
99.20 12.62 



^ Dep.l Lat. Dep. Lat.| Dep. Lat 



90.22 11.88 
91.21 12.01 
92.20 12.14 
93.20 12.27 
94.19 12.40 
95.1812.53 
96.17 12.66 
97.16 12.79 
96.15 12.92 
99.14 13.05 



P I 83 Peg. 82|Deg.'82jDeg. 



90.1712.271 91 

91.1612.41 92 

92.1512.54 93 

93.1412.68 94 

94.1312.81 95 

95.12 12.95 96 

96.11 13.08 97 

97.10 13.22J 98 

98.1013.35 99 
99.091 13.49 100 



iDep.! Lat.j 



82'Deg.|Q 



54 



TRAVERSE TABLE. 



5 


8 Deg. 


8i Deii., 


8i Deg.j 


8f Deg. 


) 


1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.99 


0.14 


0.99 


0.14 


0.99 


0.15 


0.99 


0.15 


2 


1.98 


0.28 


1.98 


0.29 


1.98 


0.30 


1.98 


0.30 


2 


3 


2.97! 0.42 


2.97 


0.43 


2.97 


0.44; 


2.97 


0.46 


3 


4 


3.961 0.56 


3.96 


0.57 


3.96 


0.69; 


3.96 


0.61 


4 


5 


4.95; 0.70 


4.96 


0.72 


4.96 


0.74 


4,94 


0.76 


5 


6j 6.941 0.84 


5.94 


0.86 


5.93 


0.89 


5.93 


0.91 


6 


7| 6.93! 0.97 


6.93 


1.00 


6.92 


1.03 


6.92 


1.06 


7 


81 7.92| 1.11 


7.92 


1.15; 7.91 


1.18 


7.91 


1.22 


8 


9 8.911 1.25 


8.91 


1.29 


8.90 


1.331 8.90 


1.37 


9 


10 9.90 1.39 


9.90 


1.43 


9.89 


1.48j( 9.88 


1.52 


10 


11110.89 1.53 


10.89 


1.68 


10.88 


1.63110.87 


1.67 


11 


1211.881 1.67|11.88 


1.72 


11.87 


1.77111.86 


1.83 


12 


1312.871 1.81 112.87 


1.87|12.86 


1.92 


12.85 


1.98 


13 


14 13.86! 1.95 113.86 


2.01 13.86; 2.07 


13.84 


2.13 


14 


15I4.85i 2.09 114.85 


2.15 14.84 2.22 


14.83 


2.28 


15 


16 15.84 2.23 


15.84 


2.30;il5.82! 2.36 


15.81 


2.43 


16 


17 16.83i 2.37 


16.83 


2.44|16.8l| 2.61 


16.80 


2.59 


17 


18 17.82; 2.51 


17.81 


2.58; 17.80 


2.66 


17.79 


2.74 


18 


1918.821 2.64 


18.80 


2.73 18.79 


2.81 


18.78 


2.89 


19 


2019.811 2.78 


19.79 


2.87; 19.78 


2.96 


19.77 


3.04 


20 


2120.80 2.92 


20.78 


3.01 20.77 


3.10 


20.76 


3.19 


21 


22 21.791 3.06 


21.77 


3.16121.76 


3.25 


21.74 


3.35 


22 


23 22.78: 3.20 22.761 3.30122.75 


3.40 


22.73 


3.50 


23 


2423.771 3.34 23.75' 3.44; 23.74 


3.65 


23.72 


3.65 


24 


25 24.76^ 3.48; 24.74; 3.59:24.73 


3.70 


24.71 


3.80 


25 


26 25,75j 3.62 


25.73; 3.T:3,.25i71; 3.84 


25.70! 3.96 


26 


27 26.74; 3.76 


26.72; 3.87 26.701 3.99 


26.69! 4.11 


27 


28 27.73, 3.90 


27.71i 4.02 27.69; 4.14 


27.67i 4.26 


28 


-29 28.72! 4.04 


28.70 4.16, 28.681 4.29 


28.66 


4.41 


29 


30 29.71! 4.18 


29.69| 4.30| 29.67 

1 1 


4.43 


29.65 


4.66 


30 
31 


3130.70; 4.31 !30.68i 4.45 30.66 


4.58 


30.64 


4.72 


32 31.69 4.45 


31.67 


4.69 31.66 


4.73 


31.63 


4.87 


32 


33 32.68 4.59 


32.66 


4.74 32.64 


4.88 


32.62 


6.02 


33 


34 33.67 4.731 33.65 


4.88 33.63 


5.03 


33,60 


5.17 


34 


35 34.66 4.87' 34.64 


6.02 34.62 


5.17 


34.59! 5.32 


35 


36 35.65 5.01 35.63 


5.17 36.60 


6.32 


35.58! 5.48 


36 


37 36.64 5.15:36.62 


5.31 36.59 


5.47 


36.57 


5.63 


37 


38 37.63 5.29137.61 


6.46 37.58! 6.62 


37.56 


5.78 


38 


39 38.62, 5.43 138.60 


6.60:38.571 5.76 


38.56 


5.93 


39 


40 39.61j 5.S7|:39.59 
4140.60 5.71 40.58 


6.74 39.561 5.91 
6.88 40.55 6.06 


39.53 


6.C8 


40 
41 


40.52 


6.24 


42 41.591 5.85' 41.57 


6.03 41.54 


6.21 


41.61 6.39 


42 


43 42.68 6.98 42.56 


6.17 42.53 


6.36 


42.60 6.54 


43 


44 43.57 6.12 43.54 


6.31 43.52 


6.50 


43.49 6.69 


44 


45 44.56, 6.26: 44.53 


6.46 44.61 6.65, 


44.48 6.85 


45 


46 45.65, 6.40; 45.52 


6.60 45.49 6.80i45.46 7.00 


46 


47 46.54 6.54 46.51 


6.74 46.48 6.96ll46.45 7.15 


47 


48 47.63; 6.68; 47.50 


6.89 47.47: 7.09;!47.44 7.30 


48 


4948.62! 6.82; 48.49 


7.03;48.46; 7.24i|48.43 7.45 


49 


60 

5 


49.511 6.96i49.48 
Dep.! Lat.liDep. 


7.17 
Lat. 


49.45 7.39! 

! 


49.421 7.61 


50 


1 1 

Dep.! Lat. 

1 


Dep.; Lat. 




82 Deg.li81fDeg. 81iDeg.l 


SliDeg. 


Q 



TRAVERSE TABLE. 



0| ®^*S' 


81 Deg. 


8i Deg. 


8f Deg. 


5' 


on 


Lat.lDep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


siWsc 


7.10 


50.47 


7.32 


50.44 


7.54 


50.41 


7.76 


51 


52 51.4S 


7.24 


51.46 


7.46 


51.43 


7.69 


51. .39 


7.91| 52 


53 52.48 


7.38 


52.45 


7.61 


52.42 


7.83 


.52.38 


8.06' 53 


54 53.47 


7.52 


53.44 


7.75 


53.41 


7.98 


53.37 


8,21j 54 


55|54.46 


7.65 


54.43 


7.89 


54.40 


8.13 


54,36 


8.371 55 


5655.46 


7.79 


55.42 


8.04 


55.38 


8.28 


55.35 


8.52! 56 


57;56.46 


7.93 


56.41 


8.18 


56.37 


8.43 


66.34 


8.67i 57 


58 57.44 


8.07 


57.40 


8.32 


57.36 


8.57 


57.32 


8,82, 58 


59,58.45 


8.21 


58.3£ 


8.47 


58.35 


8.72 


58.31 


8.981 59 


6059.42 
6160.41 


8.35 


159.38 


8.61 


59.34 


8.87 


59.30 


9.13 60 

9,28! 61 


8.49 


'60.37 


8.75 


60.33 


9.02 


60.29 


6261.40 


8.63 


61.36 


8.90 


61.32 


9.16 


61.28 


9.43 62 


63 62.39 


8.77 


,62.35 


9.04 


62.31 


9.31 


62.27 


9.58 63 


64,63.38 


8.91 


63.34 


9.18 


63.30 


9.46 


63,26 


9.74! 64 


65,64.37 


9.05 


64. 3£ 


9.33 


64.29 


9.61 164.24 


9.89 65 


66,65.36 


9.19 


65.32 


9.47 


65.28 


9.76 165.23 


10.04 66 


6766.35 


9.32 


66.31 


9.61 


66.26 


9.90 


66.22 


10.19 67 


6867.34 


9.46 


67.30 


9.76 


67.25 


10.05 


67.21 


10.34! 68 


6968.33 


9.60 


68.29 


9.90 


68.24 


10.20 


68.20 


10.50 


69 


7069.32 
7170.31 


9.74r69.28 

1 

9.88170.27 


10.04 


69.23 


10.35 


69.19 


10.65 


70 
71 


10.19 


70.22 


10.49 


70.17 


10.80 


7271.30 


10.02: 71.25 


10.33 


71.21 


10.64 


71.16 


10.95 


72 


7372.29 


10.161 72.24 


10.47 J72.20 


10.79 !72. 15 


11.10 


73 


74*73.28 


10.3073.22 


10.62.l73.19 


10.94 


73.14 


11.26 


74 


75174.27 


10.44!; 74. 22 


10.76! 


74.18 


11.09 


74.13 


11,41 


75 


76;75.26 


10.58ii75.21 


10.91! 


75.17 


11.23 


75.12 


11.56 


76 


77 


76.25 


10.72li76.20 


11.051 


76.15 


11.38 


76.10 


11.71 


77 


78 


77.24! 10. 861 


77.19 


11.19 


77.14 


11.53 


77.09 


11.87 


78 


79 


78.23 


10.99 


78.18 


11.34 


78.13 


n.68 


78.08 


12.02 


79 


80 
81 


79.22 


11.13 


79.17 


11.48 


79.12 


11.82 


79.07 


12.17 


80 
81 


80.21 


11.27 


80.16 


11.62? 


80.11 


n.97 


80.06 


12.32 


82 


81.20 


11.41 


81.15 


11.771 


81.10 


12.12 


81.05 


12.47 


82 


83 


82.19 


11.55 '82.14 


11.91 


82.09 


12.27 


82.03 


12.63 83 


84!83.18 


11.69 83.13 


12.05' 183.08 


12.42 


83.02 


12.78 84 


85 84.17 


11.83 84.12 


12.20:84.07 


12.56 


84,01 


12.93 85 


86 85.16 


ll.97j85.ll 


12.34 


85.06 


12.71 


85,00 


13.08' 86 


87 


86.15 


12.11186.10 


12.48' 


86.04 


12.86 


8.5.99 


13.23 87 


88 


87.14 


12.25 87.09 


12.63 


87.03 


13.01 


86.98 


13.39' 88 


89 


88.13 


12.39! 


88.08 


12.77! 


88.02 


13.16 


87.96 


13.54' 89 


90 
91 


89.12 


12.53 


89.07 
90.06 


12.91i 

1 


89.01 


13.30 


88.95 
89.94 


13.69! 90 
13.841 91 


90.11 


12.66 


13.06: 


90.00 


13.45 


92 


91.10 


I2.80: 91.05 


13.20 


90.99 


13.60 90.93 


14.00! 92 


93 


92.09 


12.94 92.04 


13.34 


91.98 


13.75 91.92 


14.15 93 


94 


93.09 


13.08 193.03 


13.49, 


92.97 


13.89:92.91 


14.30 94 


95 


94.08 


13.22 94.02 


13.63! 


93.96 


14.04: !93.89 


14.45' 96 


96 


95.07 


13.36 95.01 


13.78 


94.95 


[4.19!94.88 


14.60 96 


97 


96.06 


13.50] 96.00 


13.92 '95.93 


14.34 95.87 14.76 97 


98 


97.05 


13.641196.99 


14.06 96.92 


14.49 ,96.86 14.91! 98 


99 


98.04 


13.78' 


97.98 


14.21 97.91 


14.63: 97.85ll5.06' 99 


100 

CO 


99.03 
Dep. 


13.92 


98.97 


14.35 98.90 
Lat. Dep. 


14.78 

i 


98.84 15.21 lOOj 


Lat. 

! 


Dep. 


Lat. 


Dep. Lat.l 


M 


82 DegJ 


81fDeg.l'81iDeg.ll 


81 J Deg, 


=5 



56 



TRAVERSE TABLE. 



o 


9 Deg. 1 


9i Deg. 


9i Deg. 


9| Deg. 


o 


r 


Lat. 


Dep.? 


Lat.lDep. 


Lat. 
0.99 


Dep, 

0.17 


Lat. Dep. 


CO 

1 


1 


0.99 


0.16 


0.991 0.16 


0.99 


0.17 


2 


1.98 


0.31 


1.971 0.32 


1.97 


0.33 


1.97 


0.34 


2 


3 


2.96 


0,47 


2.96' 0.48 1 2.96 


0.50 


2.96 


0,51 


J 


4 


3.95 


0.63 


3.95 0.64'! 3.95 


0.66i 


3.94 


0.68 


i 


5 


4.94 


0.78 


4.93 0.80 


4.93 


0.83 


4.93 


0.85 


5 


6 


5.93 


0.94 


6.92 0.96 


6.92 


0.99 


5.91 


1.02 


6 


7 


6.91 


1.10 


6.91 L13 


6.90 


1.16 


6.90 


1.19 


7 


8 


7.90 


1.25 


7.90 1.29 


7.89 


1.32 


7.88 


1,35 


Ji 


9 


8.89 


1.41 


8.88 1.45 


8.88 


1.49 


8.87 


1,52 


9 


10 
11 


9.88 


1.56 


9.87: 1.61 
10,86 1.77 


9.86 
10.85 


1.65 


9.86 
10.84 


1,69 
1.86 


10 
11 


10.86 


1.72 


1.82 


1211.85 


1.88 


11.84 1.93 


11.84 


1.98 


11.83 


2.03 


12 


1312.84 


2.03 


12.83' 2.09 


12.82 


2.15 


12.81 


2.20 


13 


14 13.83 


2.19 


13.82! 2,26 


13.81 


2.31 


13.80 


2.37 


14 


1514.82 


2.35 


14.80] 2.41 1' 14. 79 


2.48 ,14.78 


2.54 


15 


1615.80 


2.60 


15.791 2.571 15.78 


2.641,15.77 


2.71 


16 


17 16.79 


2.66 


16.78' 2.73116.77 


2.81116.75 


2.88 


17 


1817.78 


2.82 


17,77! 2.89l|17.75 


2.97:17.74 


3.05 


18 


19 18.77 


2.97 


18.75i 3.05 


18.74 


3.14:;18.73 


3.22 


19 


20|19.75 
2l!20.74 


3; 13 

3.29 


19.74 


3.21 


|19.73 
20.71 


3.30 
3.47 


19.71 


3.39 


20 


20.73 


3.38 


20.70 


3.56 


21 


22:21.73 


3.44 


21.71 


3.64 


21,70 


3.63! 21.68 


3.73 


22 


23 22.72 


3.60 


22.70 


3.70 


22.68 


3.80' 22.67 


3.9C 


23 


2423.70 


3.75 


23.69 


3.86 


23.67 


3.96 


23.66 


4.06 


24 


25^24.69 


3.91 


24.67 


4.02 


,24.66 


4.13 


24.64 


4.22 


25 


2625.68 


4.07, 


25.66 


4.18 


i25.64 


4.29 


25.62 


4.4C 


26 


27 26.67 


4.22 


26.65 


4.34 


26.63 


4.46 


26.61 


4.57 


27 


28 27.66 


4.381 


27.64 


4.50 


i27.62 


4.62 


27.60 


4.74 


28 


29 28.64 


4.64 


28.62 


4.66 


28.60 


4.79 


28.68 


4.91 


29 


3029.63 
3l'30.62 


4.69 


29.61 
30.60 


4.82 


29.59 
30.57 


4.95 
5.12 


;29.57 
30.55 


5.08 


30 
31 


4.85' 


4.98 


5,25 


32 31.61 


5.01 


31.68 


5.14 


31.66 


5.28 


31.6'^ 


6,42 


32 


33 32.59 


5.16' 


32.57 


5.30 


32.56 


5.45i 32.52 


5,59 


33 


3433.58 


5.32!|33.56 


6.47 


33.53 


5.61 33,51 


6.76 


34 


3534.57 


5.48i!34.54 


6.63 


34.52 


5,78 34,49 


5.93 


35 


3635.56 


5.63; 


35.63 


6.79 


35.51 


6.94 35.48 


6.10 


36! 


37 36.64 


5.79 


36.52 


5,95 


36.49 


6.111136.47 


6.27 


37 


38 37.53 


5.94 


37.511 6.11 


37.48 


6.27 


137.45 


6.44 


38 


39 38.52 


6.10 


38.49 


6.27 


38.47 


6.44 


138.44 


6.60 


39 


40:39.51 


6.26 


39.48 


6.43 


39.45 

40.44 


6.60 
6.77 


39.42 


6.77 


40 

41 
42 


4ll40.50 


6.41 


40.47 


6.59 


40.41 


6.04 


4241.48 


6.57 


41.45 


6.75 


41.42 


6.92 


41.39 


7.11 


4342.47 


6.73 


43.AA 


6.91 


42.41 


7.10 


42.38 


7.28 


43 


44'43.46 


6.88 


43.43 


7.07 


43.40 


7.26 


43.36 


7.45 


44 


45'44.45 


7.04 


44.41 


7.23 


44.38 


7.43 


44.35 


7.62 


45 


46 45.43 


7.20 


45.40 


7.39 


45.37 


7,59 


45.34 


7.79 


46 


4746.42 


7.35 


46.39 


7.65 


46.36 


7,76ii46.32 


7.96 


47 


48|47.41 


7.51 


47,38 


7.72 


,47.34 


7.92 


47.31 


8.13 


48 


49 


48.40 


7.67 


48.36 


7.88 


,48.33 


8.09 


48.29 


8.30 


49 


60 


49.38 


7.82 


49.35 


8.04 


49,32 


8.26 


49.28 


8.47 


60 


CO 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep, 


Lat. 


Dep. 


Lat. 


CO 


81 Deg. 


SOfDeg. 


'80^ Deg. 


SOtDeg. 



TRAVERSE TABLE. 



9? IJeg.j ^ 



Qi 9 Deg. I 9^ Deg. 9f Deg 



Lat. Dep. r Lat. 



srso 

6251, 
53,52, 
64 53, 
55 54, 
56'55, 
57 56, 
58;57, 
5958. 
60,59. 



ereo, 

62|61, 
63;62, 
64;63, 
66'64, 
66;65. 
6766, 
6867, 
69'68, 
70:69. 



7.98 
8.13 
8.29 
8.45 
8.60 
8.76 
8.92 
9.07 
9.23 
9.39 



50.34 
51..^2 
52.31 
53.30 
54.28 
55.27 
56.26 
67.25 
58.23 
59.22 



9.54 
9.70 
9.86 
21|10.01 
2010.17 
19|l0.32 
18:10.48 
16:10.64 
1510.79 
1410.95 



60.21 
61.19 
62.18 
63.17 
64.15 
65.14 
66.13 
67.12 
68.10 
69.09 



Dep. Lat. Dep. 



Lat.Dep. f 



8.20 
8.36, 
8.52, 
8.68 
8.84 
9.00 
9.161 
9.32 
9.48 
9.64 



50.30 
51.29 
52.27 
53.26 
54.25 
55.23 
56.22 
57.20 
58.19 
59.18 



8.42;!50, 
8.58! i51, 
8.75 i52, 
8.91 53, 
9.08 :54. 
9.24 165, 
9.41 56, 
9.57 57, 
9.74 158, 
9.90|59, 



9.81 
9.97 
i0.13 
10.29 
10.45 
10.61 
10.77 
10.93 
11.09 
11.25 




60.1610.07,60 
61.1510.23161. 
62.14 10.40 !62, 
63.12 10.56 '63, 
64.11 10.73 
65.09 10.89 
66.08 11.06 
67.07 11.22 
68.05 11.39 
69.0411.55 



26 8.64' 51 

25 8.8li 52 

23 8.98 53 

22 9; 14 54' 

21 9.31 55' 

19, 9.48, 56* 

18 9.65 57! 

16' 9.82, 58, 

15' 9.99, 59 
13 10.16 60. 

1210.33! 61 
1010.60! 62 
09 10.67i 63^ 
0810.84: 64 
06 11.01 1 65 
0511.18 66 
0311.351 67 
02)11.52] 68 
0011.69| 69 
99 11.85 70 



81 80.00: 12.6!- 

82 80.99 )i;.83 
8381.9SI2.9S 
84 83.^7 ia.l4 
35 c3.95 13.30 
8684.94 13.45 
87 85.93 13.61' 
88,'66.92:i3.77 
89:87.90' 13.92 
9088.8914.08 



79.95 13.02 

80.93 13.18 
81.92113.34 
82.91]13.50 
S3.89|13.66 

84. 88! 13. 82' 
85.87|13.98 
86.86!14.15 
87.84'l4.31 
88.S3! 14.47. 



79.89 13 
80.88 13 
81.8613 
82.85 13 
83.83 14 
84. g2 14 
85.61 14 
86.79 14, 
87.78 14. 
88.77 14 



'^.97 12.02 
170.96 12.19 
71.95 12.36 
72.93 12.53 
73.92 12.70 
74.9012.87 
75.89 13.04 
76.87 13.21 
77.86 13.38 
78.84 13.55 



,37i|79.8313.72 
,53 80.82 13.89i 
,70; 81.80 14.061 
,86 82.79 14.23| 
03 83.77 14.39i 
.19 84.76 14.56] 
36 85.74 14.73' 
52' 86.73 14.90! 
69; 87.71 15.07j 
85; 88.70 15.24' 




^ Dep.i Lat. Dep.' Lat. Dep. Lat. 
^ I 81 Peg. 80|Deg. SOjDeg. 



Dep. Lat.l^J 



SOJDeg.P 



58 



TRAVERSE TABLE, 



5 


10 Deg. 1 


lO^Deg. lOiDeg. 


lOfDpg. 


-'1 


Lat. 


Dep.j 


Lat. Dep. ; Lat. Dep. 


Lat. Dep. 


1 


0.981 0.17, 


0.98 0.18 0.98 0.18 


0.98 0;i9 


1 


2 


1.97 0.35 


1.97 0.3^ 1.97 0.36 


1.96 0.37 


2 


3 


2.95 0.52 


2.95 0.531 2.95 0.65 


2.96 0.56 


3 


4 


3.94' 0.691 3.94 0.71 


3.93 0.731 


3.93 0.75 


4 


5 


4.92 


0.87 1 4.92 0.89 


4.92 


0.91 


4.91 0.93 


5 


G 


5.91 


1.04 


5,90 1.07 


5.90 


1.09 


5.89 1.12 


6 


7 


6.89 


1.22: 


6.89 1.25 


6.88 


1.28 


6.88 1.31 


7 


8 


7.88 


1.39 


7.87 1.42 


7.87 


1.46 


7.86 1.49 


8 


9 


8.86 


1.56; 


8.86 1 60 


8.85 1.64| 


8.84' 1.68 


9, 


10 


9.85 


1.74 


9.84 1.78 
10.82 1.96 


9.83 


1.82 


9.82 1.87 
10.81 i 2.05 


10 
11 


11 


10.83 


1.91 


10.82 


2.00 


12 


11.82 


2.08 


11.81 2.14 


ll.SOi 2.19] 


11.79; 2.24 


12 


13 


12.80 


2.26 


12.79 2.31 


12.78! 2.37; 


12.77: 2.42 


13 


14 


13.79 


2.431 


13.78i 2.49 


13.77 


2.65 


13.75: 2.61 


14 


16 


14.77J 2.60^ 


14.76j 2.67 


14.76 


2.73 


14.74 2.80 


15 


16 


15.76 


2.78 


15.74 2.85 


15.73 


2.92 


15.72; 2.98 


16 


17 


16.74 


2.95 


16.73' 3.O.; 


16.72 


3.10 


16.70 3.17 


17 


18 


17.73 


3.13 


17.71' 3.20 


17.70 


3.281 


17.68' 3.36 


18 


19 


18.71 


3.30 


18.70 3.38 


18.68 


3.461 


18.67J 3.54 


19 


20 
21 


19.70 


3.47 
3.65 


19.68 3.56 


19.67 


3.64 


19.65 3.73 


20 
21 


20.68 


20.66 3.74 


20.65 3.83' 20.63! 3.92| 


22 


21.67 


3.82 


21.65 3.91 


21.63 


4.01 21.61 


4.10 


22 


23 


22.65 


3.99 


22.63 4.09 


22.61 


4.19 22.60 


4.29 


23 


24 


23.64 


4.17 


23.62 4.27 


23.60 


4.37j 23.68 


4.48 


24 


25 


24.62 


4.34 


24.601 4.45:24.58 


4.56; 24.56 


4.66 


25 


26 


25.61 


4.61 


25.69| 4.63 25.56 


4.741 25.54 


4.85 


26 


27 


26.59 


4.69 


26.57' 4.S0 26.65 4.921 


26.53 5.04 


27 


28 


27.57 


4.86 


27.55 4.98 ^7.53 5.101 


27.51 5.22 


28 


29 


28.56 


5.04 


28.54 5.16'28.&V 5.28 


28.49 5.41 


29 


30 
81 


29.54 


5.21 


29.62 6.34 29.60| 5.47 
30.51 6.52'30.48| 5.65 


29.47 5.60 
3<3.46 6.78 


30 
31 


30.53 


5.38 


32 


31.51 


6.56 


31.49 5.69 31.46: 6.83 


31. 4t 5.97 


32 


33 


32.50 


5.73 


32.47 6.87 32.45: 6.01 


32.42! 6.16 


S3 


34133.43 


6.90 


33.46 6.05 33.43' 6.20| 33.401 G.u 


34 


35 


34.47 


6.08 


34.44 6.23 34.41 6.38; 34.39! 6.53 


35 


36 


35.45 


6.25 


35.43 6.41 35.40 6.66 35.37 


6.71 


36 


37 


36.44 


6.42 


36.41 6.58 36.38! 6.74136.35 


6.90 


37 


38 


37.42 


6.60 


37.39 6.76 37.36! 6.92 


37.33 


7.09 


38 


89 


38.41 


6.77 


:38.3S 6.94 38.35 


7.11 


38.32 


7.27 


39 


40 


39.39 


6.95 39.36 7.12 39.33 


7.29 


39.30 

140.28 


7.46 


40 
41 


41 


40.38 


7.12 


40.35, 7.30' 40.31 


7.47 


7.65 


42 


41.36 


7.29 


41.33' 7.47 41.30 


7.65 


:41.26 


7.83 


42 


43 


42.35 


7.47 


'42.31! 7.65: 42.28 


7.84 


42.25 


8.02 


43 


44 


43.33 


7.64 


;43.30 7.83*43.26 


8.02 


'43.23 


8.21 


41 


45 


44.32 


7.81 


'44.28 8.0L 44.25 


8.20 


44.21 


8.39 


45 


46 


45.30 


7.99 


46.27, 8.19''45.23 


8.38 


45.19 


8.58 


46 


47 


46.29 


8.16 


46.26; 8.36! 46.21 


8.57 


46.18 


8.77 


47 


48 


47.27 


8.34 


'47.23' 8.54'47.2C 


8.75 


147. 16 


8.95 


48 


49 


48.26 


8.51 


48.22 8.72't48.18 


8.93 


148.14 


9.14 


49 


5C 

CC 


49.24 


8.68 


'49.20: 8.9C 
jDep. Lat 


» 49.1fi 


9.11 


49.12 


9.33 


50 

CO 

Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


80 Deg. 


;79iDeg 


79iDeg. 


79lDeg. 



TRAVERSE TABLE. 



59 



51 


10 Deg. 


10{Deir. 


lO^Dej:. 


lO|Deg. c 


Lat. 
50.23 


Dep. 


Lat. Dep. 

50.191 9.08 


Lat. 


Dep. 


Lat. 


Dep. r" 
9.51 51 


8.86 


50.15 


9.29 


50.10 


52 


51.21 


9.03 


5L17, 9.25 


51.13 


9.48 


51.09 


9.70 52 


53 


52.19 


9-20 


52-15' 9.43 


52.il 


9.66 


52.07 


9.89 53 


54 


53.18 


9,38 


53.14 9.61 


53.10 


9.84 


53.05 


10.07 64 


55 


54.16 


9.55 


54.12 9.79 


54.08 


10.02 


54.03 


10.26 65 


56 


55.15 


9.72 


55.11 9.96 


55.06 


10.21 


55.02 


10.45 56 


57 


56.13 


9.90 


56-09110.14 


56.05 


10.39 


56.00 


10.63 57 


58 


57.12 


10.07 


57.07:10.32 


57. C3 


10.57 


56.98 


10.82' 68 


59 


58.10 


10.25 


58.06 10.50 


58.01 


10.75 


57.96 


11.00 59 


60 
61 


59.09 


10.42 


5C-04 10.68 
60.0310.85 


59.<}0 
59.98 


10.93 


58.95 


11.19 60 
11.38^ 61 


60.07 


10.59 


11.12 


59.93 


62 


61.06 


10.77 


61.0111.03 


60.96 


11.30 


60.91 


11.56 62 


63 


62.04 


10.94 


61.9911.21 


61.95 


11.48 


61.89 


11.75 63 


64 


63.03 


11.11 


62.9811.39 


62.93 


11.66 


62.88 


11,94 64 


65 


64.01 


11.29 


63.96 11.57 


63.91 


11.85 


63.86 


12.12 65 


66 


65.00 


11.46 


64.9511.74 


64.89 


12.03 


64.84 


12.31 66 


67 


65.98 


11.63 


65.9311.92 


66.8? 


12.21 


65.82 


12.50 67 


68 


66.97 


11.81 


66.91 12.10 


6b.S6 


12.39 


66.81 


12.68 68 


69 


67.95 


11.98 


67.90 12.2b 


67.84 


12.57 


67.79 


12.87 69 


70 
71 


68.94 
69.92 


12.16 


68.88 12.46 
69.8712.63 


68.83 
69.81 


12.76 


68.77 


13.06 "0^ 
13.24 71 


12.33 


12.94 


69.75 


72 


70.91 


12.50 


70.85 12.81 


70.79 


13.12 


70.74 


13.43 72 


73 


71.89 


12.68 


71.8312.99 


71.78 


13.30 


71.72 


13.62 73 


74 


72.88 


12.85 


72.82 13.17 


72. 7o 


13.49 


72.70 


13.80 74 


75 


73.86 


13.02 


73.80 13.35 


73.74 


13.67 


73.68 


13.99 75 


76 


74.85 


13.20 


74.79 13.52 


74.73 


13.85 


74.67 


14.18 76 


77 


75.83 


13.37 


75.77113.70 


75.71 


14.03 


75.65 


14.36 77 


78 


76.82 


13.54 


76.76 13.88 


76.69 


14.21 


76.63 


14.55 78 


79 


77.8C 


13.72 


77.74 14.06 


77.68 


14.40 


77. 6J 


14.74 79 


80 
81 


78.78 


13.89 


78.72 14.24 
79.71 14.41 


78.66 
79.64 


14.58 


78.60 


14.92 80^ 
15.11 81 


79.77 


14.07 


14.76 


79.58 


82 


80.75 


14.24 


80.69 14.59 


80.63 


14.94 


80.56 


15.29 82 


83 


81.74 


14.41 


81.6814.77 


81.61 


15.13 


81.54 


15.46 83 


84 


82.72 


14.59 


82.6614.95 


82.59 


15.31 


82.63 


15.67 84 


85 


83.71 


14.76 


83.6415.13 


83.38 


15.49 


83.51 


15.85 85, 


86 


84.69 


14.93 


84.63 15.30 


84.56 


15.67 


84.49 


16.04 86 


87 


85.68 


15.11 


85.6n5.48 


85.54 


15.85 


85.47 


16.23 87 


88 


86.66 


15.28 


86.6015.66 


86.5,? 


16.04 


86.46 


16.41i 88 


89 


87.65 


15.45 


87.58|l5.84 


87.61 


16.22 


87.44 


16.60 89 


90 
91 


88.63 


15.63 


88.66.16.01 
89.55il6.19 


88.49 


16.40 


88.42 
89.40 


16.791 90 
16.97 91 


S9.62 


15.80 


89.48 


16.58 


92 


90.60 


15.98 


190.53 16.37 


90.46ll6.77 


90.39 


17.16 92 


93 


91.59 


lo.lS 


91.52 16.55 


91.44 


16.95 


91.37 


17.35 93 


94 


92.57 


16.32 


92.50 16.75 


92.43 


17.13 


92.35 


17.53 94 


95 


93.56 


16.50 


93.48 16.90 


93.41 


17.31 


93.33 


17.72 95 


96 


94.54 


16.67 


94.47 17.08 


94.39 


17.49 


94..32 


17.91 96 


97 


95.53 


16.84 


95.4517.26 


95.38 


17.68 


95.30 


18.09| 97 


98 


96.51 


17.02 


96.4417.44 


96.36 


17.86 


S6.28 


18.28) 98 


99 


97.50 


17.19 


97.42 


17.621 


97.34 


18.04 


97.26 


18.47' 99 


100 

• 


98.46 


17.36 


98.40 


17.79J 


98.33 


18.22 


98.25 


18.65 100 
Lat. ^ 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


s 


80 Deg. 


79iDeg.| 


79iDeg.| 


79iDeg.p 1 



60 



TRAVERSE TABLE, 



So 

t-f- 


11 Deg.|lUDeg. 


lliDeg, 


ll|Deg.| 


si 


Lat.Dep.j 


Lat, 


Dep. 


Lat, 


Dep.' Lat. 


^ CO 

Dep. T* 


1 


0.981 0.19 




0.98 


O.So'i 0.98 


0.20 


0.98 


0.20 1 


2 


1.96 0.38 


1.96 


0.39 


1.86 


40 


L96 


0.41 2 
0.61 8 


3 


2.84 0.57 


2.94 


0.59 


2,94 


0.60 


2.84 


4 


3.93 0.76, 


3.92 


0.78 


3.92 


0.80 


3.92 


0,S2 4^ 


5 


4.91 


0.95' 


4.90 


0.98 


4.90 


1.00 1 4.80 


1.02 


5 


6 


5.89 


1.14 


5.88 


1.17 


1 5.88 


1.20il 5.87 


1.22 


6 


7 


6.87 


1.34 


6.87 


1.37! 6.86 


1.40' 6.85 


1.43 


7 


8 


7.85 1.53 


7.85 


1.56; 7.84 


1.59' 7.83 


1.63 


8 


9 


8.83 1.72 


8.83 


1.76 8.82 


1.79,1 8.81 


1.83 


9 


10 


9.82 1.91 


9.81 


1.95j 9.80 


1.99 ! 9.79 


2.04 


10 


11 


10.80 2.10 


10.79 


2.15 10.78 


2.19 10,77 


2.24 


11 


1211.78 2.29 


11.77 


2.34' 11.76 


2.39: 11.75 


2.44 


12 


1312.76 


2.48 


12.75 


2.54! 12. 74 


2.59' 12.73 


2.66 


13 
M 


14 13.74 


2.67 


13.73 


2.73113.72 


2.79^ 13.71 


2.85 


15 14.72 


2.86 


14.71 


2.93; 14.70 


2.99' 14.69 


3.C6 


15 


16115.71 


3.05 


15.69 


3.1215.68 


3.19 15.86 


3.26' 16 


1716.69 


3.24 


16.67 


3.3216.66 


3.39 16.64 


3.46| 17 


1817.67 


3.43 


17.65 


3.51 il7.64 


3.59; 17.62 


3.66! 18 


19 18.65 


3.63 


18.63 


3.71 


18.62 


3.79 18.60 


3.871 19 


20 19.63 


3.82 119.62 

1 


3.90 


19.60 


3.99; 19.58 


4.07J 20 


21 20.61 


4.01 20.60 


4.10 


!20.58 


4.19' 20.56 


4.28 21 


22 21.60 


4.20 21.58 


4.29 


21.56 


4.39"21.54 


4.48 22 


23 22.58 


4.39 22.56 


4.49 


22.54 


4.59 22.55 


4.68: 23 


24,23.56 


4.58 J23.54 


4.68 


'23.52 


4.78: 23.50 


4.89 


24 


25 24.64 


4.7:j24.52 


4.88 


24.50 


4.98: 24.48 


5.09 


26 


26125.52 


4.96 '25.50 


5,07 


'25.48 


5.18: 25.46 


6.30 


26 


27 26.50 


5.15 '26.48 


5.27 


'26.46 


6.38' 26.43 


6.50; 27 


28:27.49 


5.34 !27.46 


5.46 


27.44 


6.58 27.41 


5.70I 28 


29J28.4T 


5.5328.44 


5.66 


28.42 


5.78 28.39 


6.91| 29 
6.11 30 


30 


29,45 


5.72J!29.42 


5. §5 


29.40 


5.98 29.37 


3! 


30.43 


5.92,30.40 


6.05 


'ao.ss 


6.18' 30.35 


6.31 31 


32 


31.41 


6.1l!31.39 


6.24 


31.36 


6.38 31.33 


6.52 32 
6,72' 33 


33 


32.39 


6.30; '32.37 


6.44I 32.34 


6.58 32.31 


34 


33.38 


6.49j;33.35 


6.63 


33.32 


6.7.8 33.29 


6.92: 34 


35134.36 


6.68 134,33 


6.83 


34.30 


6.98 34.27 


7.13 35 


36 


35.34 


6.87 


35.31 


7.C2 


35.28 


7.18 '35.25 


7.33 36 


37 


36.32 


7.06 


36.29 


7.22 


36.26 


7.38 136.22 


7.53' 37 

7.74; 38 
7.94 39 


38 


37.30 


7.25 


37.27 


7.41 


37.24 


7.58 37.20 


39 


38.28 


7.44 


38.25 


7.61 i 38,22 


7.78 38,18 


40 


39.27 


7.63 


39.23 


7,80 39.20 


7.97; 39.16 

i 


8.15 40 


41*40.25 


7.82 


40.21 


8.C0 40.18 


8.17 40.14 


8.35 41 


4241.23 


8.01 


41.19 


8.19' 41.16 


8,37 41.12 


8.65 


42 


43 42.21 


8.20: 


42.17 


8.39 42.14 


8.57 '42.10 


8.76 


43 


44 43,19 


8.40 


43.15 


8.58i43.12 


8. 77, '43.08 


8.96 


44 


45 44.17 


8.59 


44.14 


8.78; 44.10 


8.97 44.06 


9.16 


45 


46 45.16 


8.78 


45,12 


8.97 45.08 


9.17:45.04 


9.37 


46 


47 46.14 


8.97 


46.10 


9.17 46.06 


9.37 46.02 


9.67 47 


4847.12 


9.16 


47.08 


9.36| 47.04 


9.57"46.99 


9.78 48 


49 48.10 


9.35 


48.06 


9. 66] 48.02 


9.77147.97 


9.98 49 
10.18 60 


6049.08 

1 


9.64 


49.04 


9.75: 49,00 


9.97 48.95 


CO 


Deg. 


Lat.! 


Dep. 

783 


Lat. Dep. 


Lat.iiDep. 

I! 


Lat.L* 

1 OQ 


s 


79 Deg. 


Deg, 


78^1 


Deg.l 


781] 


Jeg. 


21 



TRAVERSE TABLE. 




G^ 



TRAVERSE TABLE. 



o 


12 Deg.l 

1 


12iDeg. 


12iDeg. ] 
- Lat. ' Dep. 


L2f Deg.] 5-5 


En* 
1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat.lDep.'i r" 


0.98 


0.21 


0.98 


0.21 0.98' 0.22 0.98' 0.221 J 


2 


1.96 


0.42 


1.95 


0.42 1.95! 0.43 1.95 0.441 2 


3 


2.93 


0.62 


2.93 


0.64 2.93I 0.65 1 


2.93 0.66 3 


4 


3.91 0.83 


3.91 


0.85! 3.91, 0.87 { 


3.90i 0.88 4 


5 


4.89 1.04 


4.89 


I.O61 4.88 1.08 


4.88' 1.10 5 


6 


5.87 1.25 


6.86 


1.27' 5.86 1.30, 


5.85! 1.32 6 


7 


6.85! 1.46 


6.84 


1.49 6.83, 1.521 


6.83 1.54 7 


8 


7.83 


1.66 


7.82 


1.70! 7.81! 1.73 1 


7.80, 1.77 8 


9 


8.80 


1.87 


8.80 


1.91 8.79; 1.95! 


8.78! 1.99 9 


10 


9.78 


2.08, 


9.77 


2.12 


9.76 2.16; 


9.75 2.21 10 
10.73^ 2.431 11 


11110.76 


2.29^ 


10.76 


2.33 


10.74 2.38 


1211.74 2.49ill.73 


2.65 


11.72 2.60, 


11.70 2.65i 12 


1312.72 


2.70il2.70 


2.76 


12.69 2.81 


12.68 2.87' IS 


1413.69 


2.91:113.68 


2.97 13.67 3.03! 


13.65! 3.09, 14 


15' 14.67 


3.12:14.66 


3.18 14.64 3.25 


14.63 3.31 16 


16 15.65 


3.33 15.64 


3.39 15. K 3.46' 


15.61 3.53 16 


17 16.63 


3.5316.61 


3.61 16.60 3.68 


16.58 3.75 17 


18 17.61 


3.741 17.59 


3.82 17.57 3.90: 


17.56 3.97 18 


1918.58 


3.95 18.57 


4.03 18.55 4.11, 


18.531 4.19: 19 


20 19.56 


4.16! 19.54 


4.24 19.53i 4.33 

1 


19.61 


4.41 1 20 


2120.54: 4.37 20.52 


4.46 2O.6O' 4.55 


20.48 


4.63! 21 


2221.52' 4.57 21.50] 4.67 21.48 4.76 21.46' 4.86 22 


23 22.50! 4.78 22.481 4.88 22.45^ 4.98 22.431 6.08 23 


24 23.48] 4.99 23.45 5.09 23.43 5.19 23.41 6.30 24 


25 24.451 5.20 24.43' 5.30 24.41 5.41 24.38 5.62 25 


26 25.431 6.41 25.4l| 5.52 25.38 5.63 25.361 6.74 26 


27 26.41 


5.61 26.39 5.73 26.36 5.84 !26.33 6.96 271 


2827.39 


5.82 27.36' 6.&4 27.34 6.06 '27.31! 6.18 28| 


2928.37 


6.03 28.34! 6.15 28.31 6.28 


28.281 6.40 29| 


30 29.34 


6.24 29.32! 6.37 29.29; 6.49 


29.26 


6.62 30 


3130.32 6.45 30.29 6.58 30.27i 6.71 


30.24 


6.84 31 


3231.30 6.65 31.27, 6.79 31.24| 6.93 


31.21 


7.06 32 


3332.28: 6.86 32.25' 7.00 32.22' 7.14 132.19^ 7.28 331 


34 33.26! 7.07 33.5i3' 7.21 33.19 7.36 33.16 7.50 341 


35 34.24! 7.28 34.20 


7.43 34.17 7.68 34.14 7.72 35 


36 35.21' 7.48 35.18 


7.64 35.15 7.79 35.ll! '-^Si 36 


37 36.19 7.69 36.16 


7.86 36.12 8.01 36.09' 8.17' 37 


38 37.17 7,90 37.13 


8.06 37.10: 8.22 37.06 8.39 38 


39 38.15' 8.11 38.11 


8.27 38.081 8.44 38.04 8.6I1 39 


40 39.13! 8.32 39.09 


8.49 39.05; 8.63 39.01 8.83: 40 


4140.10^ 8.52 40.071 8.70 40.03! 8.87,39.99 9.05^ 41 


42 41.08' 8.73 41.04! 8.91 41.00^ 9.09 |40.96l 9.27^ 42 


43 42.06 8.94 42.02: 9.12 41.93 9.31 I41.94| 9.49i 43 


4443.04 9.15 43.00' 9.34 42.96 9.52 


42.92! 9.71! 44] 


46144.02 9.36 43.98! 9.55 43.93, 9.74 


43.89^ 9.93! 45 


46 44.99 9.56 44.95| 9.76 44.91 9.96 


44.87 10.15: 46 


47 45.97, 9.77 45.931 9.97 45.89 10.17 45.84 10.37 47 


4846.95! 9.98 46.91|10.18 46.86 10.39 46.82 10.69 48 


4947.9310.19 47.88110.40 47.8410.61 47.79 10.81! 49 


50 48.9110.40 48.86 10.61 48.81 10.82 |48.77H.03i 50 


^ Dep.' Lat.' Dep. Lat. Dep. Lat. JDep.; Lat. ^J 

M !_ to 


s 


1 78 Deg.i77|Deg. 77iDeg.i|77iDeg. S | 



TRAVERSE TABLE. 



H 



on 
51 


12 Deg. 


T2iDeg. 


121 Deg. 


12fDeg. 
Lat. Dep. 


5 

51 


Lat. 


Dep. 


Lat.lDep. 

49.&4I10.82 


Lat. 


Dep. 


49.89Jl0.60 


49.79 


11.04 49.74 11.26 


52 


50.86llO.81 


oO.Siiill.OS 


50.77 


11.25 50.72 11.48 


52 


53 


51.84!ll.02 


51.7911.25 


51.74 


11.47 51.69 11.70 


53 


54|52.82|11.23 


'52.77'll.46 


52.72 


11.69 52.67 11.92 


54 


55 53.80|11.44 


^53.75111. 67 


53. 7C 


11.90 i53.64 12.14 


55 


56154.78:11.64 


i54.72ill.88 


54.67 


12.12 54.62 12.36 


56 


57 55.75!ll.85 
58|56. 73 12.06 


155.70 


12.09 


55.65 


12.34 155.59 12.58 


57 


|56.68 


12.31 


56.63 


12.55 


56.57 12.80 


58 


59 


57.7112.27 


57.66 


12.52 


57.60 


12.77 


57.55 13.02 


59 


60 


58.69jl2.47 


58.63 


12.73 


58.58 


12.99 


58.5213.24 


60 


61 


59.67'l2 68 


59.61 


12.94 


59.55 


13.20 


59.5013.46 


61 


62 


60.6512.89 


160.59 


13.16 


60.53 


IJ.42 160.4713.68 


62 


63 


6L62 13.10 


61.57 


13.37 


61.51 


13.64 


61.45 13.90 


63 


64'62.60 13.31 


62.54 


13.58 


62.48 


13.85 


62.42 14.12 


64 


65 


63.58 13.51 


63.52 


13.79 


63.46 


14.07 


63.40 14.35 


65 


66 


64.56 13.72 


64.50 


14.00 


6^1.44 


14.29 


64.37 14.57 


66 


67 


65.54 13.93 


65.47 


14.22 


65.41 


14.50 


65.35 14.79 


67 


68 


66.5114.14 


66.45 


14.43 


66.39 


14.72 


66.32! 15.01 


68 


69 


67.49 14.35 


67.43 


14.64 


67.36 


14.93 


67..30 15.23 


69 


70 
71 


68.47 


14.55 
11.76 


68.41 


14.85 


68.34 
69.32 


15.15 


68.27^15.45 
69.2515.67 


70 
71 


69.45 


69.38!l5.06 


15.37 


72 


70.43 


14.97 


70.36:15.28 


70.29 


15.58 


70.2215.89 


72 


73 


71.40 


15.18 


71.3415.49 


71.27 


15.80 


71.2016.11 


73 


74 


72.38 


15.39 


:72.32il5.70 


72.26 


16.02 


72.1816.33 


74 


75 


73.36 


15.59 


[73.29 15.91 


73.22 


16.23j 


73.15 16.55 


75 


76 


74.34 


15.80 


74.27 16.13 


74.2c 


16.45; 


74.13:16.77 


76 


77 


75.32 


16.01 


75.25 16.34 


75.17 


16.67175.10 16.99 


77 


78 


76.30 


16.22 


76.22 16.55 


76.16 


16.88 !76.08 17.21 


78 


79 


77.27 


16.43 


77.20 16.76 


77.13 


17.10 i77.05]l7.44 


79 


80 


78.25 


16.63 


.78.18 16.97 


78.10 


17.32 78.0317.66 


80 


81 


79.23 


16.84 


79.18 17.19 


79.08 


17..53 79.00:17.88 


81 


82 


80.21 


17.05 


80.131 17.40 


80.06 


17.75 79.9818.10 


82 


83 


81.19 


17.26 


8l.llll7.61 


81.03 


17.96 SO.95! 18.32 


83 


84 


82.16 


17.46 


82.09 17.82 


82.01 


18.18 i81.93'18.54 


84 


85 


83.14 


17.67 


83.06 18.04 


82.99 


18.40 I82.90il8.76 


85 


86' 84. 12 


17.88 


84.04 18.25 


83.96 


13.61 ;83.88'1S.98 


86 


87!85.1G 


18.09 


85.02 


18.46 


84.94 


18.83 i84.85 19.20 


87 


88 86.08 


18.30 


86.00 


13.67 


85.91 


■9.65 85.83 19.42 


88 


89 87.06 


18.50 


86.97 


18.88 


86.89 


19.26 86.8119.64 


89 


90 88.03 

91 89.01 


18.71 
18.92 


87.95 
88.93 


19.10 


87.87 
88.8^ 


19.48 !S7.78:19.86 
19.70|88.76!20.08 


90 
91 


19.31 


92 


89.99 


19.13 


89.91 


19.52 


89.82 


19.91 !89.73j20.30 


92 


93 


90.97 


19.34 


90.88 


19.73 


90. SO 


iJ.13 '90.71:20.52 


93 


94 


91.95 


19.54 


91.86 


19.94 


91.77 


20.35 191.68:20.75 


94 


95 


92.92 


19.75 


92.84 


20.16 


92.75 


20.56 92.66,20.97 


95 


96 


93.90 


19.96 


93.81 


20.37 


93.72 


20.78 93.6321.19 


96 


97 


94.88 


20.17 


94.79 


20.58 


94.70 


20.99 94.6II2I.4I 


97 


98 


95.86 


20.38 


95.77 


20.79 


95.68 


21.21 ,95.58:21.63 


98 


99 


96.84 


20.58 


96.75 


21.01 


96.65 


21.43 96.56:21.85 


99 


100 

IS 


97.81 
Dep. 


20.79 
Lat. 


97.72 
Dep. 


21.22 


97.63 
Dep. 


21.64 9T.53 22.07 


100 

03 


Lat. 


Lat. 


Dep. J Lat. 


78 Deg. 


77f 


Deg. 


77iDeg.i 


77iDeg. 


Q 



u 



TRAVERSE TABLE. 



o 

1 


13 Deg. 


IS^Deg. 


ISfDeg. 


133 Deg. 


5? 

CD 
<-^ 

1 


Lat. 
0.97 


Dep. 

0.23 


Lat. Dep. 
0.97 0.23 


Lat.JDep. 
0.97^ 0.23 


Lat. 


Dep. 


0.97 


0.24 


2 


1.95 


0.45 


1.95 0.46 


I.95I 0.47 


1.94 


0.48 


2 


3 


2.92 


0.67 


2.92 0.69 


2.92 0.70 


2.91 


0.71 


3 


4 


3.90 


0.90 


3.89 0.92 


' 3.89,' 0.93 


3.89 


0.95 


4 


5 


4,87 


1.12 


4,87 1,15 


: 4.86 1.17 


4.86 


1.191 6 


6 


5.85 


1.35 


5.84 1,38 


1 5.83 


1.40 


5.83 


1.43! 6 


7 


6.82 


1.57 


6,81 1.60 


1 6.81 


1.63 


6.80 


1.66 


7 


8 


7.80 


1.80 


7.79 1.83 


7.78 


1.87 


7.77 


1.90 


8 


9 


8.77 


2.02 


8.76 2.06 


8.75 2.10 


8.74 


2.14 


9 


10 


9.74 


2.25 


9.73 2.29 


9.72 2.33 

• 


9.71 2.38 


21 


11 


10.72 


2.47 


10.71 2.52 


:10.70 2.57 


10.68 2.61 


11 


12 


11.69 


2,70 


11.68 2.75 


!ll.67, 2.80 


11.66; 2.85 


12 


13 


12.67 


2.92 


12.65 2.98 


:12.64! 3.03 


12.63 3.09 


13 


14 


13.64 


.3.15 


13.63 3,21 


13.61| 3.27 


13.60 3.33 


14 


15 


14.62 


3.37 


14.60 3.44 


14.59 3,50 


14.57 3.67 


15 


16 


15.59 


3.60 


15.57 3.67 


16,56! 3.74 


15.54 3.80 


16 


17 


16.57 


3.82 


16.55 3.90 


16.53 


3.97 


I6.51! 4.04] 17 


18 


17.54 


4.05 


17.52 4.13 


17.50 


4.20 


17.48: 4.28 18 


19 


18.51 


4.27 


18.49 4.35 


18.48 


4.44 


18.46' 4.52I 19 


20 
21 


19.49 


4.50 

4.72 


19.47 4.58 
20.44 4.81 


19.45 


4.67 


19.43 4.75 
20.40, 4.99 


20 
21 


20.46 


20.42 


4.90 


22 


21.44 


4.95 


21,41 5,04 


21,39! 5,14 


21.37' 5.23 


22 


23 


22.41 


5.17 


22,39 5.27 


22.36' 5.37 


22.34 6.47 


23 


24 


23.38 


5.40 


23.36 5.60 


23,34 6.60 


23.31; 5.70 


24 


25 


24.36 


5.62 


24.33 5.73 


24.31 


5.84 


24.28 5.94 


25 


26 


25.33 


5.85 


25.31 5.96 


25.28 


6.07 


25.25 6.18 


26 


27 


26.31 


6.07 


26.28 6.19 


26.25 


6.30 


26.23, 6.42 


27 


28 


27.28 


6.30 


27.25 6.42 


27.23 


6.54 


27.20 6.66 


28 


29 


28.26 


6.52 


28.23 6.65 


28.20 


6.77 


28.17 6.89 


29 


30 


29.23 


6.75 


29.20, 6.88 
30.17 7.11 


29.17 
30,14 


7.00 


29.14 7.13 
30.1l| 7.37 


30 
31 


31 


30.21 


6.97 


7.24 


32 


31.18 


7.20 


31.15 7.33 


31,12 7,47 


31.08 7.61 32 


33 


32.15 


7.42 


32,12 7,56 


32,09j 7.70 


32.051 7.84 33 


34 33.13 


7.65 


33.09 7.79 


33.06 7.94 


33.03' 8.08 34 


35 34.10 


7.87 


34.07i 8.02 


34.03! 8.17 


34.00, 8.32 35 


36 35.08 


8.10 


35.04 8.25 


35.01; 8.40 


34.97 8.56 36 


37 38.05 


8.32 


36,02 8.48 


35.98i 8.64 


35.94 8.79 37 


38 37.03 


8.55 


36.99 8.71 


36.95: 8.87 


36.91 9.03; 38 


39 38.00 


8.77 


37.96 8.94 


S7.92t 9.10 


37.88: 9.27 


39 


40 38.97 


9,00 


38.94, 9.17 


38.89 9.34 


38.85 9.51 


40 


4139.95 


9.22 


39.9li 9.40 


39.87' 9.57 


39.83 9.75 


41 


42 40.92 


9.45 


40.88, 9.63 


40.84' 9.80 


40.80 9.88 


^ 


43 


41,90 


9.67 


41.86 9.86 


41.8l| 10.04 


41.7710.22 


43 


44 


42.87 


9.90 


42.83 10.08 


42.7810.27 


42.74 10.46 


44 


45 


43,85 


10.12 


43.80 10.31 


43,7610,51 


43.71 10.70 


46 


46 


44.82 


10.35 


44.78,10.54 


44.7310.74 


44.6810.93 


46 


47 


45.80 


10.57 


45.75 10.77 


45.7010.97 


45.6511.17 


47 


48 


46.77 


10.80 


46.7211.00 


46.67jll,21 


46.62!ll.41 


48 


49 


47.74 


11.02 


47.7011.23 


47.65|11.44 


47.60|11.65 


49 


50 

5 


48.72 


11.25 


48.67lll.46 


48.62 11,67 


48.57 11.88 


50 


Dep. Lat. 


Dep.l Lat. 


Dep. Lat. 


Dep. Lat, 




77 


Deg. 


k^Deg. 


76iDeg. 


76iDeg. 



TRAVERSE TABLE. 



6i 



(_, 13Deg. ISfDeg 13iDeg..l3|Deg. 




66 



TRAVERSE TABLE. 





5 


14 Deg.^ 


14iDeg.|| 


14iDeg. 


M^Deg. 


to' 






Lat.j 


Dep.j 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep.j 




1 0.97 


0.24' 


0.97 


0.25' 


0.97 


0,25 


0.97 


0.25 ij 




2 1.94 


0.48: 


1.94 


0.49. 


1.94 


0.50 


1.93 


0.61 


2 




3 2.91 


0.73 


2.91 


0.74 


2.90 


0.75 


2.90 


0.76 


3 




4 3.88 


0.97 


3.88 


0.98; 


3.87 


1.00 3.87 


1.02 


4 




5 4.85 


1.21 


4.85 


1.23 


4.84 


1.25 4,84 


1.27 


£ 




6 


5.82 


1.45 


5.82 


1.48 


5.81 


l,50|i 5.80 


1.53 


6 




7 


6.79 


1.69 


6.78 


1.72 


6.78 


1.75 


6.77 


1.78 


7 




8 


7.76 


1.94 


7.75 


1.97 


7.75 


2.00 


7.74 


2.04 


8 




9 


8.73 


2.18 


8.72 


2.22 


8.71 


2.25 


8.70 


2.29 


9 




,10 
11 


9.70 
10.67 


2.42 
2.66 


9.69 


2.46| 


9.68 


2.50 


9.67 


2.55 


10 




10.66 


2.71 


10.65 


2.75 


10.64 


2.80 


11 




12 


11.64 


2.90 


11.63 


2.95 


11.62 


3.00 11.60 


3.06 


12 




13 


12.61 


3.15 


12.60 


3.-20' 


12.59 


3.25 12.57 


3.31 


13 




14 


13.58 


3.39 


13.57 


3.45; 


13.55 


3.51 


13.54 


3.56 


14 




15 


14.55 


3.63 


14.54 


3.69i 


14.52 


3.76J 


14.51 


3.82 


15 




16 


15.52 


3.87 


15.51 


3.941 


15.49 


4.011 


15.47 


4.07 


16 




17 


16.50 


4.11 


16.48 


4.18i 16.46 


4.26! 


16.44 


4.33 


17 




18 


17.47 


4.35 '17.45 


4,43 i 


17.43 


4.51:17.41 


4.581 18 




19 


18.44 


4.60 i 18.42 


4.68' 


18.39 


4.76 18.37 


4.841 19 




20'19.41 


4.84 


19.38 


4.92: 


19.36 


5.01' 19.34J 5.091 20] 




2120.38 


5.08 


20.-35 


5.I7I 


20.33 


5.26 20.31 


5.351 21 




22 21.35 


5.32 


121.32 


6.42 


21.30 


5.61 21.28 


5.6OI 22 




2322.32 


5.56 


i22.29 


6.66 


22.27 


5,76!l22.24 


6.S6i 23 




24 23.29 


5.8l!^23.26 


6.9li 


23.24 


6.01 23.21 


6.11 


24 




25124.26 


6.05 


24.23 


6.15 


24.20 


6.26124.18 


6.37 


25 




26'25.23 


6.29 


25.20 


6.40 


25.17 


6.51!125.14 


6.62 


26; 




27j26.20 


6.53 


26.17 


6.65 


26.14 


6.76|l26.11 


6.87! 27 




2827.17 


6.77 


127.14 


6.89 


27.111 7.01]127.08 


7.I3I 28 




29 28.14 


7.02 


l28.ll 


7.14 


28.081 7.26 '28.04 


7.38; 29 




3029.11 


IM 


29.08 


7.38' 


29.041 7.51 29.01 


7.64; 30 

1 




3130.08 


7.50 


I3O.O5 7.63 


30.0lt 7,76 '29.98 7.89' 31 




32 31.05 


7.74 


i31.02 7.88 


30.98J 8.01 :30.95 8.15; 32 




3332.02 


7.98;l31.98| 8.12 


3I.95I 8.26131. 91 8.40 


33 




34,32.99 


8.23132.95', 8.37 


32.921 8.51I '32.88 8.66 


34 




35,33.96 


8.47^33.921 8.62133.89' 8.76^33.85! 8.91 


35 




36 34.93 


8.71 


,34.891 8.86 34.85' 9.01 


!34.81 9.17 


36 




37 35.90 


8.95 


,35.861 9.11 35.821 9.26 


|35.781 9.42! 37 




38;36.87 


9.19 


36.831 9.35 36.79| 9.51 


36.75 9.671 38 




39137.84 


9.44 


37.80i 9.60 


37.76 9.76 


37.71 9.93I 39 




40 38.81 


9.68 


38.771 9.85 


38.73 10.02 


:38.6810.18 40 




41|39.78 


9,92 


39.7410.09 


39.69 10.27 


|39.65'l0.44! 41 




4240.75 


10.16 140.71 10.34 


40.66ll0.52 


i40.62!l0.69' 42 




4341.72 


10.40' '41.68 10.68 


41.63il0.77 


141.5810.95 43 
42.55:11.20 44 




44 42.69 


10.64" 42.65 10.83 


42.6C 


11.02 




45 43.66 


10.89; 143.62 11.08 


43.57 


11.27 


43.5211.46 45 




46 44.6i: 


11.13 


I44.5B 11.32 


44.63 


11.52 


4^1.4811.71 46 




47 45.60 11.3' 


j45.5511.67 


45.5C 


11.77 


45.45,11.97 47 




48 46.67 11.61 


46.52 11.82 


46.4' 


12.02 


46.4212.22 48 




49i47.5411.85'|47.49,12.06 


47.44 


12.27 


47.39 12.48 49 




5 

-•- 


48.5lll2.10 48.4612.31 

- 1 11 1 


48.41 


12.52 


48.3512.73 60 




; Dep 


.JLat 


.|Dep.|Lat. 


Dep 


Lat. 


Dep.| Lat 






^ 7C 


DegJ753DBg. 


ll75fDeg. 


75iDeg 



TRAVERSE TABLE. 



6? 



a 

So" 
51 


14 Deg. 


HiDeg.j 


Hi Deg. 


1 45 Deg. 


2 

So 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dpe. 


Lat. 


Dep. 




49.49 


12.34 


49.43 


12.55 


49.38 


12.77 


49.32 


12.98 


51 




52;50.46 


12.58 


50.40 


12.80 


50.3413.02 


50.29 


13.24 


52 




53i51.43 


12.82 


51.37 


13.05 


51.31113.27 


51.25 


13.49 


53 




5452.40 


13.06 


62.34 


13.29 


52.28113.52 


52.22 


13.75 


54 




55i53.37 


13.31 


53.31 


13.54 


53.25113.77 


53.19 


14.00 


55 




56,54.34 


13,55 


54.28 


13.78 


54. 22 1 14. 02 


54.15 


14.26 


56 




57,55.31 


13.79 


55.25 


14.03 


55. is; 14.27 


55.12 


14.51 


57 




58 56.28 


14.03 


56.22 


14.28i 


56.15,14.52 


56.09 


14.77 


58 




5957.25 


14.27 


57.18 


14.52: 


57.12tl4.77 


57.06 


15.02 


59 




60 58.22 

1 

6159.19 


i4.52j 


58,15 


14.77| 


58.09 15.02 
59.06'l5.27 


58.02 


15.28 


60 
61 




14.76: 


59.12 


15.021 


58.99 


15.53 




6260.16 


15.00 


60.09 


15.251 


60.03115.52 


i59.96 


15.79 


62 




63 61.13 


15.24' 


61.06 


15,51 


60.99 15.77 


|60.92 


16.04 


63 




64 62.10 


15.48 


62.03 


15.75; 


61.9616.02 


61.89 


16.29 


64 




65 63.07 


15,72 


63.00 


16.00 


62.9316.27 


j62.86 


16.55 


65 




66 64.04 


I5.97i 


63.97 


16.25 


63.90 16.53 


63.83 


16.80 


66 




67 65.01 


16.21 


6494 


16.49 


64.87 16.78 


164.79 


17.06 


67 




68 65,9S 


16.45 


65.91 


16,74 


65.83 17.03 


|65.76 


17.31 


68 




69:66,95 


16.69' 


66.88 


16.98 


66.80 17.28 


166.73 


17.57 


69 




70|67.92 
71'68.89 


16.93| 


67.85 


17.23 


67.77 17.53 
68.7417.78 


67.69 


17.82 


70 
71 




17.18' 


68.82 


17.48 


68.66 


18.08 




72:69.86 


17.42! 


69.78 


17.72 


69.7118.03 


169.63 


18.3S 


72 




73!70.83 


17.66 


70.75 


17.97| 


70.67 18.28 


'70.59 


18.59 


73 




74 71.80 


17.90 


71.72 


18.22 


71.64 18.53 


71.56 


18.8^ 


74 




io,72.77 


18.14; 


72.68 


18.46 


72.61 18.78 


72.53 


19.10 


75 




76|73.74 


18.39 


73.66 


18.711 


73.58 19.03 


73.50 


19.35 


76 




77174.71 


18.63 


74.63 


18.95: 


74.55 19.28 


74.48 


19. 6C 


77 




78 


75.68 


18.87 


75.60 


19.20: 


75.52 19.53 


75.43 


19.86 


78 




79 


76.65 


19.11 


76.57 


19.45 i76.48 19.78 


76.40 


20.11 


79 




80 
81 


77.62 


19.35 


77.54 


19.69| 77.45 20.03 
19.94! 78.4220.28 


77.36 


20.37 


80 
81 




78.59 


19.60 


78.51 


78.33 


20.62 




82 79.56 


19.84 


79.48 


20. 18ii79.39 20.53 


79.30 


20.88 


82 




83 80.53 


20.08| 


80.45 


20.43! 80.36 20.78 


80.26 


21.13 


83 




84 81.50 


2O.32I 


81.42 


20.681 81.32 21.03 


81.23 


21.39 


84 




85 82.48 


20.56! 


82.38 


20.92 82.29 21.28 


182.20 


21.6-^ 


85 




8683.45 


20.81 


83.35 


21.17 83.26 21.53 


83.17 


21.90 


86 




87|S4.42 


21.05 


84.32 


21.42 84.23 21.78 


84.13 


22.15 


87 




88:85.39 


21.29 


85.29 


21.66 85.20 22.03 


85.10 


22.41 


88 




8986.36 


21.53 


86.26 


21.91' 


86.17 22.23 


86.07 


22.68 


89 




90 87.33 

91 88.30 


21.77J 


87.23 


22.15, 


87.13|22.53 
88.10,22.78 


87.03 


22.91 


90 
91 




22.011 


68.20 


'22.40 


86.00 


23.17 




92 89.27 


22.26: 


89.17 


22.65 


89,07 23.04 


88.97 


23.42 


92 




93 90.24 


22..50i 


90.14 


22.89 


90.04 23.29 


89.94 


23.68 


93 




94 91.21 


22.741 


91.11 


23.14 


91.01 23.54 


90.90 


23.93 


94 
95 




95 92.18 


22.98' 


92.08 


2-3.381 


91.97 23.79 


91.87 


24.19 




96 93.15 


23.22 


93.05 


23.63! 


92.9424.04 


92.84 


24.44 


96 


97194.12 


23.47, 


94.02 


23.88i 


93.9124.29 


93.80 


24.70 


97 


98 


95.09 


23.711 


94.98 


24.12 


94.88 24.54 


94.77 


24.95 


98 




99 


96.06 


23.951 


95.95 


2i.37j 


95.85 24.79 


95.74 


25.21 


99 




100 

CO 

5 


97.03 


24.19 


96.92 


24.62 


96.81 ;25.04 
Dep.! Lat. 


96.70 


25.46 


100 

CO 

Q 




Dep. 


Lat. 


Dep. 


Lat.l 


Dep. Lat. 




76 Deg. 


75|Deg.| 


75iDeg. 


75iDeg. 





m 



TRAVERSE TABLE. 



s 

1 


15 Deg. 


IS^Deg.j 


ISiDeg. 


laiDe?. 


5 

on' ■ 

irt- 

1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.97 


0.26 


0.96 


0.26 


0,96 


0.27 


0.96 


0.27 


2 


1.93 


0.52 


1,93 


0.53 


1,93 


0.53 


1.92 


0.54 


2 


3 


2.90 


0.78 


2.89 


0.79 


2,89 


0.80 


2.89 


0.81 


3 


4 


3.86 


L04 


3.86 


1.05 


3.86 


1.07 


3.85 


1.09 


4 


5 


4.83 


1.29 


4.82 


1.32 


4.82 


1.34 


4.81 


1.36 


5 


6 


6.80 


1.55 


6.79 


1,58 


6.78 


1.60 


5,77 


1.63 


6 


7 


6.76 


1.81 


6.75 


1.84 


6.75 


1.87 


6.74 


1.90 


7 


8 


7.73 


2.07 


7.72 


2.10 


7.71 


2.14 


7.70 


2.17 


8 


9 


8.69 


2.33 


8.68 


2.37 


8.67 


2.41 


8.66 


2.44 


9 


10 
11 


9.66 


2.59 


9.65 
10.61 


2.63 


9.64 


2.67 


9.62 


2.71 


10 
11 


10.63 


2.85 


2.89 


10.60 


2.94 


10.59 


2,99 


.12 


11.59 


3.11 


11.58 


3.16 


11.66 


3.21 


11.56 


3.26 


12 


13 


12.56 


3.36 


12.54 


3.42} 


12,63 


3.47 


12.51 


3.63 


13 


14 


13.62 


3.62 


13.61 


3.681 


13.49 


3.74 


13.47 


3.80 


14 


15 


14.49 


3.88 


14.47 


3.95i 


14,45 


4,01 


14,44 


4.07 


15 


16 


15.45 


4.14 


15.44 


4.21 


16,42 


4.28 


16.40 


4.34 


16 


17 


16.42 


4,40 


13.40 


4.47 


16.38 


4„54 


16.36 


4.61 


17 


18 


17.39 


4.66 


17.37 


4,73 


17.35 


4.81 


17.32 


4.89 


18 


19 


18.35 


4,92 


18.33 


5.00 


18,31 


5.08 


18.29 


6.16 


19 


20 
21 


19.32 


6.13 


19.30 


6.26 


19,27 


5.34 


19.25 


6.43 


20 
21 


20.28 


5,44 


20.26 


5..62 


20.24 


6,61 


20.21 


5.70 


22 


21.26 


5.69 


21.23 


6.79 


21.20 


5.88 


21.17 


5.97 


22 


23 


22.22 


6.95 


22.19 


6.05 


22.16 


6.16 


22.14 


6.24 


23 


-24 


23.18 


6.21 


23.15 


6.31 


23.13 


6.41 


23.10 


6.61 


24 


25 


24.15 


6.47 


24.12 


6.58 


24.09 


6.68 


24.06 


6.79 


25 


26 


25.11 


6.73 


aj.08 


6.84 


26.05 


6.95 


26.02 


7.06 


26 


27 


26.08 


6.99 


26.06 


7.10 


26.02 


7.22 


25.99 


7.33 


27 


28 


27.06 


7.25 


27.01 


7.36 


26.98 


7.48 


26.95 


7.60 


28 


29 


28.01 


7,61 


27.98 


7.63 


27.95 


7.75 


27.91 


7.87 


29 


30 
31 


28.98 


7.'?6 


28.94 


7.89 


28.91 


8.02 


28.87 


8.14 
8.41 


30 
31 


29.94 


8.02 


29.91 


8.15 


29.87 


8,28 


29.84 


32 


30.91 


8.28 


,30.87 


8.42 


30.84 


8,56 


30.80 


8.69 


32 


33 


31.88 


8.54 


31.84 


8.B8 


31.80 


8.82 


31.76 


8.96 


33 


34 


32.84 


8.80 


32.80 


8.94 


32.76 


9.09 


32.72 


9.23 


34 


35 


33.81 


9.06 


33.77 


9.21 


33.73 


9.36 


33.69 


9.60 


35 


36 


34.77 


9,32 


34.73 


9.47 


34.69 


9.62 


34.65 


9.77 


36 


■37 


35.74 


9.68 


35.70 


9.73 


35,65 


9.89 


35.61 


'-O.O-: 


37 


38 


36.71 


9.84 


36.66 


10.00 


36.62 


10.16 


36.57 


10.31 


38 


39 


37.67 


10.09 


37.63 


10.26 


37.58 


10.42 


37,54 


10.59 


38 


40 


38.64 


10.35 


38,69 


10.52 


38.55 


10.69 


38,50 


10.86 


40 


41 


39.60 


10,61 


39,56 


10.78 


39.51 


10.96 


39,46 


11.13 


41 


,42 


40.57 


10,87 


40.52 


11.05 


40.47 


11.22 


40,42 


11.40 


42 


43 


41.53 


11.13 


41.49 


11.31 


41.44 


11.49 


41.39 


11.67 


43 


44 


4^50 


11.39 


42.45 


11.67 


42.40 


11,76 


42,35 


11.94 


44 


45 


43.47 


11,65 


43.42 


11.84 


43.36 


12,03 


43,31 


12.2] 


45 


46 


44.43 


11.91 


44.38 


12.10 


44.33 


12.29 


44,27 


12.49 


46 


47 


45.40 


12.16 


45.36 


12.36 


45.29 


12.56 


46,24 


12.76 


47 


48 


46.36 


12.42 


146.31 


12.63 


46.25 


12.83 


46.20 


13.03 


48 


49 


47.3S 


12,68 


;47.27 


12.89 


47.22 


13.09 


47.16 


13.30 


49 


:60 


48.30 


12,94 


148.24 


13.15 


48.18 


13.36 


48.12 


13.67 


60 


Dep. 


Lat, 


iDep. 


Lat, 


Dep. 


Lat. 


Dep. 


Lat. 


en 

5 


75 Deg. 


' 74iDeg 


.74fDeg. 


74iDeg. 



TRAVERSE TABLE 




TRAVERSE TABLE. 




TRAVERSE TABLE. 



71 



p. 

51 


16 Deg. 


le^Deg. 


16i 


Deg. 


le^Deg. 


51 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 
48.90 


Dep. 

14.48 


Lat. 


Dep. 
14.70 


49.02 


14.06 


48.96 


14.27 


48.84 


5ii 


49.99 


14.33 


49.92 


14.55 


49.86 


14.77 


49.79 


14.89 


55 


5ii 


50.95 


14.61 


50.88 


14.83 


50.82 


16.05 


50.75 


15.27 


Bf. 


54 


51.91 


14.88 


51.8415.11 


51.78 


15.34 


51.71 


15.56 


M 


55 


52.87 


15.16 


52.80 


16.39 


52.74 


15.62 


52.67 


15.85 


5.^. 


56 


53.83 


15.44 


53.76 


15.67 


53.69 


15.90 


53.62 


16.14 


56 


57 


54.79 


15.71 


54.72 


15.95 


54.65 


16.19 


54.58 


16.43 


57 


58 


55.75 


15.99 


55.68 


16.23 


55.61 


16.47 


55.64 


16.72 


58 


69 


56.71 


16.26 


56.64 


16.51 


56.57 


16.76 


56.50 


17.00 


59 


60 
61 


57.68 


16.54 


57.60 


16.79 


67.53 


17.04 


57.46 


17.29 
17.58 


60 
61 


68.64 


16.81 


58.56 


17.07 


58.49 


17.32 


58.41 


62 


59.60 


17.09 


59.52 


17.35 


59.45 


17.61 


59.37 


17.87 


62 


6S 


60.56 


17.37 


60.48 17.63 


60.41 


17.89 


60.33 


18.16 


63 


64 


61.52 


17.64 


61.44ll7.91 


61.36 


18.18 


61.28 


18.44 


64 


65 


62.48 


17.92 


62.40il8.19 


62.32 


18.46 


62.24 


18.73 


65 


66 


63.44 


18.19 


63.3618.47 


63.28 


18.74 


63.20 


19.02 


66 


67 


64.40 


18.47 


64.32 18.75 


64.24 


19.03 


64.16 


19.31 


67 


68 


65.37 


18.74 


65.28:19.03 


65.20 


19.31 


65.11 


19.60 


68 


69 


66.33 


19.02 


66.24| 19.31 


66.16 


19.60 


66.07 


19.89 


69 


70 
71 


67.29 


19.29 
19.57 


67.20 


19.59 


67.12 


19.88 
20.17 


67.03 
67.99 


20.17 
20.46 


70 
71 


68.25 


68.16 


19.87 


68.08 


72 


69.21 


19.85 


69.12 


20.15 


69.03 


20.45 


68.95 


20.75 


72 


73 


70.17 


20.12 


70.08 


20.43 


69.99 


20.73 


69.90 


21.04 


73 


74 


71.13 


20.40 


71.04 


20.71 


70.95 


21.02 


70.86 


21.33 


74 


75 


72.09 


20.67 


72.00 


20.99 


71.91 


21.30 


71.82 


21.61 


76 


76 


73.06 


20.95 


72.96 


21.27 


72.87 


21.59 


72.78 


21;90 


76 


■77 


74.02 


21.22 


73.92 


21.55 


73.83 


21.87 


73.73 


22.19 


77 


78 


74.98 


21.50 


74.88 


21.83 


74.79 


22.15 


74.69 


22.48 


78 


79 


75.94 


21.78 


75.84 


22.11 


75.75 


22.44 


75.66 


22.77 


79 


80 
81 


76.90 


22.05 
22.33 


76.80 


22.39 
22.67 


76.71 


22.72 


76.61 

77.56 


23.06 


80 


77.86 


77.76 


77.66 


23.01 


23.34! 8l| 


82 


78.82 


22.60 


78.72 


22.95 


78.62 


23.29 


78.52 


23.63 


82 


83 


79.78 


22.88 


79.68 


23.23 


79.58 


23.57 


79.48 


23.92 


83 


84 


80.75 


23.15 


80.64 


23.51 


80.54 


23.86 


80.44 


24.21 


84 


85 


81.71 


23.43 


81.60 


23.79 


81.50 


24.14 


81.39 


24.50 


85 


86 


82.67 


23.70 


82.56 


24.07 


82.46 


24.43 


82.35 


24.78 


86 


87 


83.63 


23.98 


83.52 


24.35 


83.42 


24.71' 


83.31 


26.07 


87 


88 


84.59 


24.26 


84.48 


24.62 


84.38 


24.99 


84.27 


25.36 


88 


89 


85.55 


24.53 


85.44 


24.90 


85.33 


25.28 


85.22 


25.66 


89 


90 
91 


86.51 


24.81 


86.40 


25.18 
25.46 


86.29 


25.56 


86.18 
87.14 


25,94 
26.23 


90 
91 


87.47 


25.08 


87.36 


87.25 


25.85 


92 


88.44 


25.36 


88.32 


25.74 


88.21 


26.13, 


88.10 


26.51 


92 


93 


89.40 


25.63 


,89.28 


26.02 


89.17 


26.4ll 


89.06 


26.80 


93 


94 


90.36 


25.91 


00.24 


26.30 


90.13 


26.70' 


90.01 


27.09 


S4 


95:91.32 


26.19 


91,20 


26.58 


91.09 


26.98' 


90.97 


27.38 


95 


96 


92.28 


26.46 


92.16 


26.86 


92.05 


27.27 


91.93 


27.67 


96 


97 


93.24 


26.74 


93.12 


27.14 


93.01 


27.55: 


92.88 


27.95 


97 


98 


94.20 


27.01 


94.08 


27.42 


93.96 


27.&3 


93.84 


28.24 


98 


99 


95.16 


27.29 


95.04 


27.70 


94.92 


28.12' 


94.80 


28.53 


99 


100 


96.13 


27.56 


96.00 


27,98 


95.88 


28.40 


95.76 


28.82J100 


CO 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 1 ^• 

1 CO 


74 Deg. 


73^Deg. 


73^1 


Deg.l 


73^1 


I>eg. 


«| 



n 



TRAVERSE TABLE. 



o 


TTC 


eg. 


IT^Deg. 


IT^Deg. 


17fDeg. 


CO 


en 

1 


Lat. 

0.96 


Dep. 


Lat. Dep. 


Lat. i Dep. 


Lat. Dep. 


0.29i 


0.95: 0.30 


0.95 


0.30 


0.95 


0.30 


1 


2 


1.91 


0.58 


1.91 0.59 


1.91 


0.60 


1.90 


0.61 


2 


3 


2.87 


0.83! 


2.87 0.89 


2.86 


0.90 


2.86 


0.91 


3 


4 


3.83 


1.17: 


8.82 1.19 


3.81 


1.20 


3.81 


1.22 


4 


5 


4.78 


1.46 


4.78: 1.48 


4.77 


1.50 


4.76 


1.52 


6 


6 


5.74 


1.75 


5.73 1.78 


5.72 


1.80 


5.71 


1.83 


6 


7 


6.69 


2.05i 


6.691 2.08 


6.68 


2.10 


6.67 


2.13 


7 


fi 


7.65 


2.34 


7.64| 2.37 


7.63 


2.41 


7.62 


2.44 


8 


9 


8.61 


2.63; 


8.60 2.67 


8.58 


2.71 


8.57 


2.74 


9 


10 
11 


9.56 


'2.92 


9.55 


2.97 


9.54 


3.01 


9.52 


3.05 


IQ 


10.52 


3,22! 


10.51 


3.26 


10.49 


3.31 


10.48 


3.35 


12 


11.48 


3,51 


11.46 


S.56 


11.44 


3.61 


11.43 


3.66 


12 


13 


12.43 


3.80 


12.42 


3.85 


12.40 


3.91 


12.38 


3.96 


13 


14 


13.39 


4.09 


13.37 


4.15 


13.35 


4.21 


13.33 


4.27 


14 


15 


14.34 


4.39 


14.33 


4.45 


14.31 


4.51 


14.29 


4.57 


15 


16 


15.30 


4.68 


15.28 


4.74 


15.26 


4.81 


15.24 


4.88 


16 


17 


16.26 


4.97 


16.24 


6.04 


16.21 


5.11 


16.19 


6.18 


17 


18 


17.21 


5.26 


17.19 


5.34 


17.17 


5.41 


17.14 


5.49 


18 


19 


18.17 


5.56 


18.15 


5.63 


18.12 


5.71 


18.10 


5.79 


19 


20 


19.13 


5.85 


19.10 


5.93 


19.07 


6.01 


19.05 


6.10 


20 
21 


21 


20.08 


6.14 


20.06 


6.23 


20.03 


6.31 


20.00 


6.40 


2'i 


21.04 


6.43 


21.01 


6.52 


20.98 


6.62 


20.95 


6.71 


22 


2a 


21.99 


6.72 


21.97 


6.82 


21.94 


6.92 


;21.91 


7.01 


2? 


24 


22.95 


7.02 


22.92: 7.12 


22.89 7.22 


i22.86 


7.32 


24 


25 23.91 


7.31 


23.881 7.41 


23.84 


7.52 


[23.81 


7.62 


25 


26 24.86 


7.60 


24.83] 7.71 


24.80 


7.82 


124.76 


7.9a 


26 


27 25.82 


7.89 


l25.79| 8.01 


25.75 


8.12 


25.71 


8.2s 


27 


38 26.78 


8.19 


26.74J 8.30 


26.70 


8.42 


26.67 


8.54 


28 


29 27.73 


8.48 


i''i7.70| 8.60 


i27.66 


8.72 


27.62 


8.84 


2.9 


30 28.69 
S129.65 


8.77 


l28.65i 8.90 

1 


|28.61 


9.02 


28.57 


9.15 


31 


9.06 


:29.6l': 9.19 


29.57 


9.32 


29.52 


9.45 


32 30.60 


9.36 


30.56, 9.49: '30.52 


9.62 


30.48 


9.76 


32 


33131.56 


9.65 


:31.52| 9.79|31.47 


9.92 


31.43 


10.06 


33 


34:32.51 


9,94 


;32.47 10.08:32.43 


10.22 


32.38 


10.37 


34 


35 33.47 


10.23 


33.43 10. 38 i '33.38 


10.52 


33.33 


10.67 


35 


36 34.43 


10.53;|34.38 10.68 34.33 


10.83 


34.29 


10.98 


36 


3735.38 


10.82 |35.34 10.97! 33.29' 1 1. 13| 135.24 


11.28 


37 


38j36.34 


11.11 


36.29 11.27136.2411.43 


36.19 


11.68 


3S 


39|37.30 


11.40 


37.25 11.57; 37.19jll.73 


37.14 


11.89 


39 


40 
41 


38.25 


11.69 


138.20 11.86 38.15|12.03 
i39.16Jl2.16 39.1o!l2.33 


38.10 
39.05 


12.19 


41 


39.21 


11.99 


12.50 


42 


40.16 


12.28 


J40.llil2.45; 40.06 12.63 


40.00 


12.80 


42 


43 


41.12 


12.57 


l41.07|12. 75 41.01 12.93 


40.95 


13.11 


43 


44 


42.08 


12.86 


'42.02 13.05 41.96il3.23 


41.91 


13.41 


4^1 


46 


43.03 


13.16 


!42.98; 13.34! 42.92 


13.53 


42.86' 


13.72 


45 


46 


43.99 


13.45 


,43.93 13. 64; 43.87 


13.83 


43.81 


14.02 


46 


47 


44.95 


13.74 


[44.89 13.94 


;44.82 


14.13 


44.76 


14.33 


47 
48 


48 


45.90 


14.03 


45.84 14.23 


!45.78 14.43 


45.71 


14.63 


49 


46.86 


14.33 


46.80] 14.53 


46.73 


14.73 


46.67 


14.94 


49 


60 

.22 


47.82 
Dep. 


14.62 


47.75 14,83 
Dep. Lat. 


47.69 


15.04 
Lat. 


47.62 
Dep. 


15.24 


_50 

m 


Lat. 


Dep. 


Lat. 


73 ] 


Deg. 


72|Deg. 


72iDeg. 


72iDeg. 


Q 



TRAVERSE TABLE. 




74 



TRAVERSE TABLE. 



5 


18 Deg. 


ISfDeg. 


IsfDeg. 


18|Deg. 


S' 


1 


Lat. 
0.95 


Dep. 
0.31 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 1 Dep. 


0.95 


0.31 


0.95! 0.^ 


O.gsi 0.32 


1 


2 


1.90 


0.62 


1.90l 0.63 


1.90: 0.63 


1.89i 0.64 


2 


3 


2.85 


0.93 


2.851 0.94 


2.84: 0.95 


2.841 0.96 


3 


4 


3.80 


1.24 


3.80i 1.25 


3.79' 1.27 


3.79! 1.29 


4 


5 


4.76 


1.55 


4.75; 1.57 


4.74 1.69 


4.731 1.61 


5 


6 


5.71 


1.85 


5.70 1.88 


5.691 1.90 


5.63 1.93 


6 


7 


6.66 


2.16 


6.65 2.19 


6.64i 2.22 


6.63 2.25 


7 


8 


7.61 


2.47 


7.60 2.51 


7.59! 2.54 


7.581 2.57 


8 


9 


8.56 


2.78 


8.55 2.82 


8.53 2.86 


8.52 


2.89 


9 


10 


9.51 


3.09 


9.50 3.13 


9.48; 3.17 
10.43 3.49 


9.47 
10.42 


3.21 
3.54 


10 
11 


11 


10.46 


3.40 


10.45 3.44 


12 


11.41 


3.71 


11.40 3.76 


11.38 3.81! 


11.36 


3.86 


12 


13 


12.36 


4.02 


12.35 4.07 


12.33 4.I2I 


12.31 


4.18 


13 


14 


13.31 


4.33 


13.30 4.38 


13.28 4.44, 


13.26 


4.50 


14 


15 


14.27 


4.64 


14.25 4.70 


14.22 4.76; 


14.20 


4.82 


16 


16 


15.22 


4.94 


15.20 5.01 


15.17 5.08i 


15.15 


5.14 


16 


17 


16.17 


5.25 


16.14 5.32 


16.12: 5.39 


16.10 


5.46 


17 


18 


17.12 


5.56 


17.09 5.64 


17.071 5.71 


17.04 


5.79 


18 


19 


18.07 


5.87 


18.04 5.95 


18.021 6.03 


17.99 


6.11 


19 


20 
21 


19.02 


6.18 
6.49 


18.99 6.26 
19.94 6.58 


118.97 6.35! 

! — : — 1 

119.91 6.66' 


18.94J 6.43 
19.89| 6.75 


20 
21 


19.97 


22 


20.92 


6.80 


20.89 6.89 


120.86 6.98! 


20.83 7.07 


22 


23 


21.87 


7.11 


21.84 7.20 


21.81 7.30i 


21.78, 7.39 


23 


24 


22.83 


7.42 


22,79 7.52122.76: 7.62| 


22.73 7.71 


24 


25 


23.78 


7.73 


23.74 7.831 i23.71i 7.93 


23.67; 8.04 


25 


26 


24.73 


8.03 


2469 8.14; 124.66 8.25 


24.62 8.36 


26 


27 


25.68 


8.34 


25.64 8.46' 125.60: 8.57 


25.57! 8.68 


27 


28 


26.63 


8.65 


26.59 8.77 


26.55 8.88 


26.51 9.00 


28 


29 


27.58 


8.96 


27.54 9.08 


127.50, 9.20 


27.46 9.32 


29 


30 


28.53 


9.27 


28.49 9.39 


128.45 9.52 


28.41 9.64 


30 


31 


29.48 


9.58 


29.441 9.71 


29.40 9.84 


29.35' 9.96 


31 


32 


30.43 


9.89 


30.39 10.02 


130.35 10.15 


30.30 10.29 


32 


33 


31.38 


10.20 


31.34 10.33 131.29 10.47 


31.25 10.61 


33 


34 


32.34 


10.51 


32.29 10.65 132.24 10.79 


32.20 10.93 


34 


35 


33.29 


10.82 


33.24 10.96 


33.19 11.11 


33.14 11.25 


35 


36 


34.24 


11.12 


34.19 11.27 


34.1411.42 


34.09 11.67 


36 


37 


35.19 


11.43 


35.1411.59 


35.0911.74 


36.0411.89 


37 


38 


36.14 


11.74 


36.09 11.90 


36.04 12.06 


35.98 12.21 


38 


39 


37.09 


12.05 


37.04 12.21 


36.98 12.37 


36.93 12.54 


39 


40 
41 


38,04 
38.99 


12.36 
12.67 


37.9912.53 

1 

38.9412.84 


37.93 12.69 
'38.88 13.01 


37.8812.86 


40 
41 


38.82 13.18 


42 


39.94 


12.98 


39.89,13.15 


39.83 13.33 


39.7713.50 


42 


4340.90 


13.29 


40.84113.47 


40.78 13.64 


40.72 13.82 


43 


44 41.85 


13.60 


41.79 13.78 '41.73 13.96 


41.6614.14 


44 


45 42.80 


13.91 


42.74;i4.09; 42.67 14.28 


42.61 14.46 


45 


46 


43.75 


14.21 


43.69:14.41! 43.62 14.60 


43.56 14.79 


46 


47 


44.70 


14.52 


44. 64' 14.72! i44.57 14.91 


44.5115.11 


47 


4S!45..65 


14.83 


45.59il5.03 


45.52 15.23 


45.4515.43 


48 


49146.60 


15.14 


46.54il5.35 


146.47 15.55 


46.401 15.75 


49 


60 


47.55 
Dep. 


15.45 
Lat. 


47.4! 
Dep 


i 15.66 


!47.42 15.87 


47.35 18.07 


50 


. Lat. 


Dep. Lat. 


Dep. Lat. 


CO 

Q 


72 Deg. 


n^Deg. 


7HDeg. 


|71iDeg. 



TRAVERSE TABLE. 




■76 



TRAVERSE TABLE. 





19 Deg. 


T9iD^ 


19iDeg." 


19^Deg.| 


00 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep, 


Lat. 


Dep. 


1 


0.95 


0.33 


0.94 


0.33 


0.94 


0.33 


0.94 


0.34 


1 


2 


1.89 


0.66 


1.89 


0.66 


1.89 


0.67! 


1.88 


0.68 


2 


3 


2.84 


0.98 


2.83 


0.99 


2.83 


1.00 


2.82 


1.01 


S 


4 


3.78 


1.30 


3,78 


1.32 


3.77 


1.34 


3,76 


1.36 


4 


5 


4.73 


1.63 


4.72 


1.65 


4.71 


1.67, 


4.71 


1.69 


5 


6 


5.67 


1.95 


5.66 


1.98 


5.66 


2.00 


5.65 


2.03 6 


7 


6.62 


2.28 


6.6i: 2,31! 


6.60 


2.34 


6.59 


2.37 7 


8 


7.56 


2.60 


7,65 


2.64 


7.54 


2.67! 


7.53 


2.701 8 


9 


8.51 


2.93 


8,50 


2.971 


8.48 


3.00 


8.47 


3.041 9 


10 
11 


9.46 
10.40 


3,26 


9.44 
10,38 


3.30j 


9.43 
10.37 


3.34 
3.67 


9.41 
10.35 


3.38| 10 
3.72 11 


3.68 


3.631 


12 


11.35 


3.91 


11,33 


3.96 jll.31 


4.01 


11.29 


4.06: 12 


13 


12.29 


4.23 


12,27 


4.29! 12.25 


4.34 


12.24 


4.39 13 


14113.24 


4.66 


13.22i 4.621 i 13.20 


4.67 


13.18 


4.73! 14 


16] 14. 18 


4.88 


14.16 4.95 


14.14 


5.01 


14.12 


6.07! 15 


16 


15.13 


5.21 


15.111 5.28 


15.08 


5,34 


16.06 


5.41! 16 


17 


16.07 


5.53 


16.05: 6.60 


16.02 


6.67 


16.00 


5,74| 17 


18 


17.02 


6.86 


I6.99| 5.93: 


16.97 


6.01 


16.94 


6.08! 18 


19 


17.96 


6.19 


17.94 6.26| 


17.91 


6.34 


17.88 


6.42 19 


20 
21 


18.91 
19.86 


6.51 
6.84 


18.88 
19.83 


6,69 
6,92 


18.85 


6.68 


18.82 


6,76j 20 


19.80 


7.01 


19.76 


7,10l 21 


22 


20.80 


7.16 


20.77 


7.25 


20.74 


7.34 


20.71 


7,43 


22 


23 


21.75 


7.49 


21.71 


7,68 


21.68 


7.68 


21.66 


7,77 


23 


24!22.69 


7.8IH22.66 7.91 


22.62 


8.01 


22.59 


8,11 


24 


25 23.64 


8.14i|23.60 8.24 


23,57 


8.36 


23.53 


8,45 


25 


2624.68 


8.46:i24.55 8.67 


24.61 


8.681 124.47 


8.79 


26 


27:25.53 


8.79:i25.49i 8.90 


25.45 


9.01125.41 


9.12 


27 


28 26.47 


9.12!26.43i 9.23 


26.39 


9.35126.36 


9.46 


28 


2927.42 


9.44J27.38 


9.56 


27.34 


9.681 !27.29 


9.80: 291 


3028.37 


9.771 128.32 

ji 


9.89 


28.28 


10.01 


128.24 


H).14 


30 


3129.31 


lO.O9ll29.27 


10.22 


I29.22 


10.35 


29.18 


10,48 


31 


32I3O.26 


10.42 :30.21 


10.55 


30.16 


10.68 30.12 


10,81 


32 


33|31.20 


10.74 31.15 


10.88 31.11 


11.02 31.06 


11.15 


33 


34 32.15 


11.07 32.10 


11.21 32.05 


11.35 32,00 


11.49 


34 


35i33.09 


11.39,33.04 


11.64 ,32.99 


11,68 


32.94 


11.83 


35 


36,34.04 


11.72133.99 


11.87i33.94 


12.02 


33.88 


12.17 


36 


37:34.98 


12.06: 34.93 


12.20 |34.88 


12.35 


34.82 


12.50 


37 


3835.93 


12.3735.88 


12.63 '35.82 


12.68 35.76 


12.84 


38 


3936.88 


12.70 36.82 


12.86 136.76 


13,02 36.71 


13.18 


39 


40J37.82 
41 38.77 


13.02 
13.35 


37.76 


13.19 


37.71 


13.36; 37.66 


13.62 


40 


38.71 


13.52 


38.65 


13.69 38.59 


13.86 


41 


42 39.71 13.67 39.65 


13.85 i39.59 


14.02 39.63 


14.19 


42 


43 40.66|14.00ii40.60il4.18 ;40.53 


14.36! 40.47 


14.63 


43 


44 41.60! 14.32 41.54il4.51 41.48 


14.69 41.41 


14.87 


44 


4542.65114.65 l42.48114.84 42.42 


15.02 42.36 


16.21 


45 


46 43.49! 14.98 43.43:15.17 |43.36 


15.36 43.29 


16.54 


46 


47 44.44:15.30 i44.37l5.50 


44.30 


15.69] 44.24 


16.88 


47 


48 45.3815.63 45.3215.83 


45.25 


16.02! 45.18 


16.22 


48 


49 46.33.15.93 46.26 16.15 


46.19 


16.36: 46.12 


16.56 


49 


5047.28' 16.28 '47.20 16.48 

i 1 : I 


47.13 


16.69 


47.06 


16.90 


50 


tg 


!Dep.[Lat. JDep.i Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


CO 


5 


71 Deg. ^703Deg. 


70iDeg,l 


70iDeg. 



TRAVERSE TABLE. 



IQiDegJ 193Deg. 




Lat.Dep. 



48.0017.23 51 



48.94 17.57 
49.88 17.91 
50.82 18.25 
51.76 18.59 
!52.71 18.92 
53.65 19.26 
54.59 19.60 
55.5319.94 59 
66.47120.27 60 



.29; 63 
.63 64 
65' 



70 



85.65 30 
86.5931 
87.5331 
88.47 31 
89.4132 
90.3532 
91.29 32 
92.24 33 
93.18 33 
94.1233 



^ Dep. Lat. ,Dep. Lat.j 

S I 71 Peg. I70 3 Peg. 701 Peg. 



Pep. I Lat. 



70 'Peg. 



87 



91 
92 
93 
94 
95 
96 
97 
98 
99 
100 



78 



TRAVERSE TABLE. 



s 

ft- 

1 


20 Ueg. 


20-1 Des;. 


26^Deg, 


20jDeg. 


2 

1 


Lat. 
0.94 


Dep. 
0.S4 


Lat. 
0.94 


Dep, 

0.35 


Lat. 
0.94 


Dep. 
0.35 


Lat. 
0.94 


Depi 


0.35 


2 


1.88 


0.68 


1.88 


0.69 


1.87 


0.70 


1.87 


0.71 


2 


3 


2.82! 1.031 


2.81 


1,04 


2.81 


1.05 


2.81 


1.06 


3 


4 


3.76 


1.37 


3.75 


1.38 


3.75 


1.40 


3.74 


1.42 


4 


5 


4.70 


1.71 


4.69 


1.73 


4.68 


1.75 


4.68 


1.77 


5 


6 


5.64 


2.05 


5.63 


2.08 


6.62 


2.10 : 5.61 


2.13! 6 


7 


6.58 


2.39, 


6.57 


2.42 


6.56 


2.45 I 6.55 


2,48 7 


6 


7.52 


2.74, 


7.51 


2.77 


7.49 


2.80 7.48 


2.831 g 


9 


8,46 


3.08; 


8.44 


3.12 


8,43 


3.15 8.42 


3,19 


9 


10 
11 


9.40 3,42, 

— 1 — ! 

10.34! 3,76 


9,38 


3.46 


9.37 


3.50 9,35 


3.54 


10 


10,32 


3,81 


10.30 


3.85 10.29 


3.90 11 


12 


11,281 4.10 


11,26 


4.15 


11.24 


4.20 11.22 


4,25 12 


13 


12.221 4.45 


12.20 


4.50 


12.18 


4.55 12.16 


4,61: IS 


14 


13,16: 4.79 


13.13 


4.86 


13.11 


4.90 13.09 


4.96 14 


15 


14,10i 5.13 14.07 


5.19 


14.05 


6.25 14.03 


5,311 15 


1615.04! 5.47 


15,01 


5.54 


14.99 


5.60 14.96 


5.67 K 


iri5.97i 5.81 


15.95 


5.88 


15.92 


6.95 15.90 


6,02 17 


1816.91; 6.16 


16,89 


6.23 


16.86 


6.30 16.83 


6.36 18 


19 17.851 6.50 


17,831 6.58 


17.80 


6.65 17.77 


6.73 19 


20 
21 


18.79 


6.84! 


18,76 6.92 


18.73 


7.00 18.70 


7.09 20 


19.73 


7.18 


19, 70! 7.27 


19.67 


7.35 19.64 


7.44 21 


22 


20,67^ 7.52 


20.64! 7,61 


20.61 


7.70 20,57 


7.79 22 


2321.61: 7.87121.58 7.96 


21.54 


8,05 21.51 


8.15 23 


24 22.55 8.21 '22.52: 8.31 


22.48 


8.40 22.44 


8.50 24 


2523.49: 8.55 23.45 8.65 


23.42 


8.76 23.38 


8.86 25 


2624.43! 8.89 24.39 9.00 


24.36 


9.11 24.31 


9.21 26 


2725.37 9.23 25.33. 9.36 


26.29 


9.46 25.26 


9.57 27 


28 26.311 9.58 26.27 9.69 


26.23 


9.81 26.18 


9.92 28 


29 27.25i 9.92 27.21 10.04 


27.16 


10.16 27.12 


10.27 29 


30 28.19 10.26 


28. 15i 10.38 


28. 10 


10.51 28.06 


10.63 30 


31 29.13 10.60 


29,08 10.73 


29.04 


10.86 28.99 


10.98 31 


32 30.07 10.94 30.02 11.08 


29.97 


11.21 29,92 


11.34 32 


3331.01 11.29 30.96 ll.*i 


30,91 


11,56 30,86 


11.69 33 


3431.95 11.63 31.9011.77 


3i.86 


11.91 31.79 


12,05 34 


35 32.89 11.97 32.84 12.1] 


32.78 


12.26 32.73 


12,40 35 


36 33.83 12.31 33.77 12.46 


33.72 


12.61 33.66 


12,75 36 


37 34.77 12.65 34.71| 12.81 


34.66 


12.96 34.60 


13.11 37 


38 35.7113.1)0 35.65|18.15 


36.69 


13.31 35.54 


13.46 38 


3936.65 13,34 36.59 13.50 


36.53 


13.66 36.47 


13.82 39 


40!37.59 13.68 37.53! 13.84 


37.4? 


14.01 37.41 


14.17 40 


4138.53 14.02 38.47 14.19 


38.40 


14.36 38.34 


14.53 41 


42 39.47 14,36 39.4014.54 


39.34 


14.71 39.28 


14.88 42 


43 40.4114.71 4G.34il4.8s 


40.28 


16.06 40.21 


15.23 43 


4441.35 15.05 41.28,16.28 


41.21 


15.41 41.15 


15.59 44 


45 42.29 15.39 42.22:15.68 


42.16 


15.76 42.08 


15.94 45 


46 43.2315.73 42.16:15.92 


43.09 


16.11 43.02 


16.30 46 


47 44.17 16.07 44.09il6.27 


44.02 


16.46 43.95 


16.65: 47 


48 45.11 16.42 45.03 16.61 


44.96 


16.81 44.89 


17.01 


48 


49 46.0416.76 45,97116.96 


46.90 


17.16 45,82 


17.36 


49 


5046.9817.10 46.91117.31 


46.83 
Dep. 


17,51 46.76 


17,71 


50 


^ Dep.' Lat. 

en 


Dep,l Lat. 


Lat. 


Dep.| 


Lat. 




,70 


Deg.i 


693 Deg. 


69iDeg.| 


69lDeg. 


s 



TRAVERSE TABLE. 




so 



TRAVERSE TABLE, 



t3 


21 Deg. 


21iDeg. 


21^Deg. 


21 4^ Deg. 


2 
1 


I 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat.jDep. 
0.93 0.37 


0.93 


0.36 i 0.93 


0.36 


0.93 


0.37 


2 


1.87 


0.721 1.86 


0.72 


1.86 


0.73 


1.86 0.74 


2 


3 


2.80 


1.081 ! 2.80 


LOS- 


2.79 


1.10 


2.79; 1.11 


3 


4 


3.73 


1.43 : 3.73 


1.45 


3.72 


1.47 


3.72 1.48 


4 


6 


4.67 


1.79 


i 4.66 


L81 


4.66 


1.83 


4.64 


1.85 


5 


6 


5.60 


2.15 


1 5.59 


2.17 


6.58 


2.20 


5.57 


2.22 


6 


7 


6.54 


2.61 


1 6.52 


2.64 


6.51 


2.57 


6.50 


2.69 


7 


8 


7.47 


2.87 


' 7.46 


2.90 


7.44 


2.93 


7.43 


2.96 


8 


9 


8.40 


3.23 8.39 


3.26 


8.37: 3.30 


8.36 


3.34 


9 


10 


9.34 


3.68 


9.32 


3.62 


9.30i 3.67 


9.29 


3.71 


10 


11 


10.27 3.94 


10.251 3.99 


10.231 4.03 


10.22 4.08 


11 


12 


11.20 4.30 


11.18| 4.35 


11.17; 4.40 


11.16 4.45 


12 


13 


12.14 4.66 


12.12; 4.71 


12.10! 4.76 


12.07 4.82 


13 


14 


13.07 5.02 


13.051 5.07 


13.03] 6.13 


13.00 6.19 


14 


15 14.0iD 5.38! 13.98! 6.44 


13.9(81 6.50 


13.93 5.66 


15 


16 14.04 6.73 


14.91 5.80 


14.891 5.86 


14.86! 5.93 


16 


17,15.87 6.09 


15.841 6.16 


15.82: 6.23 


15.79! 6.30 


17 


18 16.80 6.45 


16.78 6.52 


I6.75! 6.60 


16.72 


6.67 


18 


19|17.74] 6.81 


117.711 6.89 


17.68| 6.96 


17.66 


7.04 


19 


2018.671 7.17 


{18.64! 7.25 


18.61J 7.33 


18.58 


7.41 


20 


21 19.6l| 7.53 


19.67i 7.61 


19.54! 7.70 


19.50 


7.78 


21 


22'20.54j 7.88 


20.50' 7.97 


20.47! 8.06 


20.43 


8.15 


22 


23 21.47' 8.24 


21.44i ^.34 


21.40: 8.43 


21.36 


8.52 


23 


24 


22.41; 8.60 


22.371 8.70 


22.33: 8.80 


22.291 8.89 


24 


25 


23.34; 8.96 


23.30; 9.06 


23.26| 9.16 


23.22! 9.26! 25] 


26 


24.271 9.32 


24.23i 9.42 


24.191 9.53 


24.15! 9-63 


26 


27 


25.21i 9.68 


,25.16i 9.79 


25.12! 9.90 


25.0810.01 


27 


28 


26.1410.03 


26.10:10.15 


26.05! 10.26 


26.0110.38 


28 


29 


27.0710.39 


27.0310.51 


26.98 10.63 


26.94^10.75! 29] 


30 
31 


28.0110.75 


27.961 10.87 


27.91 11.00 
28.84 11.36 


27.86 


11.12| 30 
11.49 31 


28.9411.11 


28.8911.24 


28.79 


32 


29.87;11.47 


29.82:11.60 


29.77111.73 


29.72 


11.86 32 


33 


30.8ljll.83 


30.7611.96 


30.7012.09 


30.65 


12.23 33 


34 


31.7412.18 


31.6912.32 


31.6312.46 


31.58 


12.60 34 


35 


32.68! 12.54 


32.62 12.69 


32.56:12.83 


32.51 


12.97] 35 


36 


33.61 1 12.90 33.55 13.05i 


33.50 13.19 


33.44 


13.341 36 


37 


34.5413.26 


34.4813.41' 


34.43 13.56 


34.37 


13.71 37 


38 


35.48;13.62 


35.4213.77: 


35.3613.93 


35.29 


14.08: 38 


39 


36.41il3.98 


;36.35 14.14136.2914.29 


36.22!14.45; 39 


40 


37.3414.33 


37.28il4.60: 


37.22,14.66 
38.1515.03 


37.15 14.82 40 
38.0815.191 41 


41 


38.28] 14.69 


38.2114.86 


42 


39.2l!l5.05 


39.14il5.22i39.08il5.39 


39.0l|l6.56| 42 


43 


40.14 15.41 


40.08 15.58 140.0115.76 


39.9415.931 43 


44 


41.08! 15.77: 41.01: 15.95 140.94; 16. 13i 


40.8716.30 44 


45 


42.01 16.13:|41.94 16.31 


41,87 16.49 


41.80'16.68' 45 


46 


42.9416.48il42.87;l6.67: 


42.8016.86 


42.73 17.05' 46 


47 


43.88 16.841 i43.80:i7.03 


43.73il7.23 


43.65 17.42 47 


48 


44.81 


17.20 


|44. 74] 17.40 


44.6617.69 


44.58 17.79 


48 


49 


45.75 


17.56 


45.67 17. 76| 


45.59!l7.96 


45.5118.16 


49 


50 


46.68 


17.92 


46.6018.12! 

1 i 


46.52 18.33 


46.4418.53 


50 


en 

Q 


Dep. 


Lat. 


Dep.l Lat.' 


Dep. Lat. 


Dep. Lat. 


to 

Q 


69 Deg. 


68 3 Deg. i 


aS^Deg. 


68iDeg. 



TRAVERSE TABLE. 



81 



{-,21 Deg.21iDeg.;i21^Deg. 



r*j Lat. Dep. ] Lat. Dep. ! Lat. Dep. 



47.63 18.48 
I4S.46 18.85 
49.40 19.21 
50.33 19.67 
51.26 19.93 
52.19 20.30 
53.1220.66 
.54.06 21.02 
54.99 21.38 
55.92 21.73 



47.45 18. 
48.38 19. 
49.31 19. 
50.24 19. 
61.17 20. 
62.10 20. 
63.03 20. 
53.96 21. 
54.89 21. 
65.83 2L 



,21peg. 



Lat. Dep. 



69 47.37 
06 48.30 : 
42;, 49.23: 
79i;50.16: 



60 



61 56.95;21.86 

62 57.88 22.22 

63 58.82'22.58 

64 59.75 22.94 
63 60.68 23.29 

66 61.62 23.65 

67 62.55 24.01 

68 63.48 24.37 

69 64.42 24.73 

70 65.85 25.09 



7166. 

72 67. 

73 68. 

74 69, 

75 70. 

76 70. 

77 7L 
7872. 
79.7S, 

80 74. 

81 tZ 

82 76. 

83 77. 

84,78. 

85 79. 

86 80. 

87 81. 
68 82. 

89 83. 

90 84. 



.28 26.44 
,22 26.80 
,15 26.16 
,08 26.52 
,02 26.88 
,95 27.24 
89 27.59 
,82 27.93 
,75 28.31 
,69 28.67 

,62 29.03 
55 29.39 
,49 29.74 
,42 30.10 
35 30.46, 
29 30.82 
22 31.18 i 
16 31.54 
09 31.89 
0232.25 



9184.96 32.61 

92 85.89 32.97 

93 86.82 33.33 

94 87.76 33.69 

95 88.69 34.04 

96 89.62 34.40 

97 90.56 34.76 

98 91.49 35.12 

99 92.42 33.48 
100 93.36 35.84 

♦: iDep.t Lat. 
.2 



84.8^32.98 
86.7433.34 
86.68 33.71 
87.6134,07 
88.54134.43 
89.47!34.79 
90.40 35.16 
91.34!33.52 
92.27i35.88 
93.20J36.24 



]73.36 29.69l 
] 76.29 30.05 i 

[77.22 30.42|i 
178.16 30.79!! 
79.09 31.1511 
180.02 31.52! 
180.95 31. 89 1: 
!61.8832.23;i: 
182.81 32.62, i| 
|83.7432.99;|i 

184.67 33.35 
185.6033.72 
186.53 34.08 
87.46 34.45 
'88.39 34.82 
89.32 35.18 
90.25 35.56 
91.18 35.92 
92.11 36.28i 
93.04 36.65j 

! Dep.' Lat. 



.87; 86 

;.24| 87, 

1.61 i 88 

:.98 89 

1.36 90 



Q 69 Deg.i68£Deg. 'eS^Deg. 



84,62 33.' 
185.45 S4.( 
!86.38 34.^ 
|87.31 34.( 
188.2435.5 
|89.17 35.i 
90.09 35.J 
91.02 36.J 
91.95 36.{ 
92.88 37.C 



98 
99 
100 



16 



Dep. Lat. 



TBAVERSE TABLE 




TRAVERSE TABLE, 




84; 



TRAVERSE TABLE. 



o 
s 

r* 


23 Deg. 


23iDeg. 


j23|Deg.l|23aDeg. 


0' 


Lat. Dep. 


Lat. Dep. 


;Lat. 


Dep. i: Lat. 


Dep. 


1 


0.92 0.39 


0.92] 0.39 


j 0.92 


0.40 1 0.92 


0.40 


1 


2 


1.84| 0.78 


1.84| 0.79 


1 1.S3 


0.80 


1.88 


0.81 


2 


3 


2.76 1.17 


2.76i 1.18 


i 2.75 


1.20; 


2.75 


1.21 


3 


4 


3.68 1.66 


3.681 1.68 


3.67 


1.59 


3.66 


1.61 


4 


6 


4.60| 1.95 


4.691 1.97 1 4.59 


1.99 


4.58 


2.01 


6 


6 


6.52! 2.34 


5.611 2.3711 6.60 


2.39: 


6.49 


2.42 


7 


6.44 2.74 


6.43| 2.76 1 6.42 


2.79 


6.41 


2.82 


7 


8 


7.36, 3.13 


7.35 3.16|i 7.34 


3.19 


7.32 


3.22 


8 


9 


8.281 3.52 


8.27 3.56 


i 8.26 


3.69; i 8.24 


3.62 


9 


10 
11 


9.20 8.91 
10.13' 4.30 


9.19 3.96 
10.11 4.34 


9.17 
,10.09 


3,99 
4.39 


9.15 


4.03 


Id 
11 


10.07 


4.43 


1211.05 


4.69 


ll.OSi 4.74 


11.00 


4.78 1.0.98 


4.83 


13 


13 11.97 


5.08 


11.941 6.13 


11.92 


6.181)1.90 


6.24 


13 


1412.89 


5.47 


12.861 6.631 12.84 


6.58! 12.81 


5.64 


U 


15 13.81 


6.86 


13.78: 6.92! 13.76 


6.98j 13.73 


6.04 


15 


16! 14.731 6.25i 


14.70! 6.32 14.67 


6.381 14,64 


6.44 


16 


17 16.65 6.64i 


15.62 6.71. 15.69 


6.781.15.56 


6.85 


17 


18 16.67 i 7.03| 


16.54 7.11 16.61 


7.18116,48 


7.25 


18 


19 17.49 


7.42 


17.46 7.501117.42 


7,68 17.39 


7,65 


19 


20j 18.41 
2119.33 


7.81 
8.21 


18.38 7.89 
19.29; 8.29 


1 18.34 


7.97 


18.31 


8,05 


20 
21 


i 19.26 


8.37 


19.22 


8,46 


22 20.25 


8.60 


20.21; 8.681 20.18 


8.7-7 


20.14 


8,86 


22 


23 21.17^ 8.99 


21.13 9.08! 21.09 


9.17 


21,05 


9.26 


23 


24 22.091 9.38. 


22.05, 9.47 22.01 


9.67 


21,97 


9.67 


24 


25 23.01 9.77 


22.97 9.87:^22.93 


9.97 


22,88 


10,07 


25 


26 23.93 10.16 


23.89 10.26123.84 


10.37 


23,80! 10.47 


26 


27,24.86 10.56 


24.81 10.66! 24.76 


10.77 


24.7110.87 


27 


28 


25.77 10.94 


25.7311.05 25.68 


11.16 


26.6311.28 


28 


29 


26.69; 11.33 


26.64 11.45| 26.59 


11.66 


26.64ill.68 


29 


SO 
31 


27.62ill.72 

1 

28.6412.11 


27.66 11.84:27.51 


11.96 


27.46 12.08 
28,37 12,49 


SO 
SI 


28.48 12.24 I28.43 


12.36 


32 


29.4612.60 


29.40 12.63 [29.35 


12.76 


29,29:12.89 


32 


33 


30.38 12.89 


30,32,13.031130.26 


13.16 


30.2113.29 


SS 


34 


31.3013.28 


31.24|13.42!!31.18 


13.,56 


31,1213,69 


34 


35 


32.22,13.68 


32.16,13.82 32.10 


13.96 


32.04; 14. 10 


35 


S6 


33.14114.07 


33.08 14.21:33.01 


14.35 


32.9514,50 


36 


37 


34.06114.46 


34.00 14.61 !33.93 


14.75 


33.8714,90 


87 


S8 


34.98|l4.86 


34.91 15.001 34.86 


15.15 


34.7816,30 


88 


39 


35.90115.24 


35.83 16.39,' 135.77 


15,55 


36,70 15,71 


39 


40 


36.82 


15.63 


36.76 


16.79 36.68 


15.96 


36.61 16.11 


40 


41 


37.74 


16.02 


37.67 


16.181 |S7.60 


16.36 


37.6316,61 


41 


42 


38.66116.41 


38.59 16.58138.52 


16.75 


38.4416.92 


42 


43 

44 


39.68116.80 
40.60117.19 


39.51 


16.97; 39,43 
17.37:40.35 


17.16 

17,54 


39,36!l7.32 
40.2717.72 


43 
44 


40.43 


45 


41.42117.58 


41.36 17.76 141.27 


17.94 


41.1918.12 


45 


46 


42.34 17.97 


42.26 18,16,42.18 


18.34 


42,10:18.53 


46 


47i 43.26 18.36 


43.18 18.55; 43.10 


18,74 


43.02! 18.93 


47 


48 


44.18,18.76 


44.1018.96 44.02 


19.14 


43.9319.33 


48 
49 


49 


45.10119.16 


45.02 19.34! 144.94 


19.54 


44.85:19,73 


6Q 


46.03 
Dep^ 


19.64 




46.94 19.74 


I45.85 

1 


19.94 


45.77 20.14 


60 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. Lat. 


■s 


67 Peg. 


m^Veg. 


iee^Peg.l 


66iDeg.S| 



TRAVERSE TABLE. 



85 



t:j|23 Deg 




3G 



TRAVERSE TABLE, 



c 

«-»■ 
1 


24 Deg. 


24J^Deg. 


r24^Deg. 


24^ Deg, 


2 

So* 
1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat, 


Dep. 


0.91 


0.41 


0.91 


0.41 


0.91 


0.41 


0,91 


0.42 


9 


1.8f 


0.81 


1.82 


0.82 


1.82 


0.83 


1.82 


0.84 


9 


8 


2.74 


1.22 


2.74 


1.23 


2.73 


1.24 


2.72 


1,26 


3 


4 


3.65 


1.63 


3.65 


1.64 


3.64 


1.66 


3.8£ 


1.67 


4 


,5 


4.57 


2.03 


4.56 


2.05 


4.56 


2,07 


4.64 


2,0£ 


6 


6 


5.48 


2.44 


3.47 


2.46 


6.46 


2.49 


5.45 


2,51 


6 


7 


6.39 


2.85 


6.38 


2.87 


6.37 


2,90 


6.36 


2,9S 


7 


R 


7.31 


3.25 


7.29 


3.29 


7.28 


3.32 


7.27 


3.55 


fi 


9 


8.22 


3.66 


8.21 


3.70 


8.19 


3,73 


8.17 


3,77 


P 


10 
11 


9.14 
10.05 


4.07 
4.47 


9.12 


4.11 


9.10 
10.01 


4,16 

4,56 


9.08 


4,19 


10 


10.03 


4.52 


9.9& 


4,61 


11 


19 


10.96 


4.88 


10.94 


4.93 


10.92 


4,98 


10.90 


5,02 


19 


13 


11.88 


6.29 


11.85 


5.34 


11.83 


6,39 


11.81 


5,44 


1.S 


14 


12.79 


6.69 


12.76 


6.75 


12,74 


6.81 


12.71 


5,86 


14 


15 


13.70 


6.10 


13.68 


6.16 


13.66 


6.22 


13.62 


6,28 


15 


18 


14.62 


6.51 


14.59 


6.57 


14.56 


6.64 


14.53 


6.70 


16 


17 


15.53 


6.92 


15.60 


6.98 


15,47 


7.05 


15.44 


7.12 


17 


18 


16.44 


7.32 


16.41 


7,39 


16,38 


7.46 


16.35 


7.54 


18 


19 


17.36 


7.73 


17.32 


7.80 


17.29 


7,88 


17.25 


7.95 


19 


20 
91 


18.27 
19.18 


8.13 


ia24 

19.15 


8.21 
8.63 


18.20 
19.11 


8.29 
8.71 


18.16 
19,a7 


8,37 


20 
21 


8.54 


8.79 


99 


20.10 


8.95 


20.06 


9.04 


20.02 


9.12 


19.98 


9,21 


29 


93 


21.01 


9.35 


20.97 


9.45 


20.93 


9.64 


20.89 


9,63 


'23 


94 


21.93 


9.76 


21.88 


9.86 


21.84 


9,95 


21.50 


10,05 


24 


95 


22.84 


10.17 


22.79 


10.27 


22.75 


10.37 


22.70 


10.47 


95 


96 


23.75 


10.58 


23.71 


10.68 


23.66 


10.78 


23.61 


10.89 


26 


97 


24.67 


10.98 


24.62 


11.09 


24.57 


11.20 


24.52 


11.30 


27 


98 


26.58 


11.39 


25.56 


11.50 


25.48 


11,61 


25.43 


11.72 


28 


99 


26.49 


11.80 


26.44 


11.91 


26.39 


12,03 


26.34 


12.14 


29 


80 


27.41 


12.20i 


27.35 


12.32 


27.30 
28.21 


12.44 
12.86 


27.24 
28.16 


12.56 

12.98 


30 
31 


31 


28.32 


12.61 


28.26 


12.73 


32 


29.23 


13.02 


29.18 


13.14 


29.12 


13.27 


29,06 


13,40 


39 


33 30.15 


13.42 


30.09 


13.66 


30.03 


13.68 


29.97 


13.82 


33 


34 


31.06 


ia.83 


31.00 


13.96 


30.94 


14.10 


30.88 


14.23 


34 


35 


31.97 


14.24 


31.91 


14.38 


31.85 


14.51 


31.78 


14.66 


35 


3fi 


32.89 


14.64 


32.82 


14.79 


32.76 


14.93 


32.69 


15.07 


3fi 


37 


33.80 


15.05 


33.74 


16.20 


33.67 


15.34 


33.60 


15,49 


37 


38 


34.71 


15.46 


34.65 


13.61 


34,68 


15,76 


34,61 


15.91 


38 
39 


39 


35.63 


15.86 


35.66 


16.02 


35,49 


16.17 


35.42 


16,33 


40 


36.54 


16.27 


36.47 
37.38 


16.43 

16.84 


36.40 
37,31 


16,69 

17,00 


36.33 
37,23 


16.75 
17.16 


40 


41 


37.46 


16.68 


41 


49 


38.37 


17.08 


38,25 


17.26 


38.22 


17,421 


38,14 


17,68 


42 


43 


39.28 


17.49 


39.21 


17.66 


39.13 


17.83] 


39.05 


18.00 


4% 


44 


40.20 


17.90 


40.12 


18.07 


40.04 


18.25 


39,96 


18.42 


44 


45 


41.11 


18.30 


41.03 


18.48 


40.95 


18,66 


40.87 


18,84 


45 


4« 


42.02 


18.71 


41.94 


18.89 


41.86 


19.08 


41.77 


19.26 


46 


47 


42.94 


19.12 


42.85 


19.30 


42.77 


19.49 


42.68 


19.68 


47 


48 


43.85 


19.52 


43.76 


19.71 


43.68 


19.91 


43.59 


20.10 


4£( 


49 


44.76 


19.93 


44.68 


20.13 


44.69 


20.32 


44.50 


20.51 


49 


30 

s 


46.68 
Dep. 


20.34 
Lat. 


45.59 


20.64 


45.50 
Dep. 


20.73 
Lat, 


45.41 


20.93 


5Q 

CD 

5 


Dep. 


Lat. 


Dep. 

65^1 


Lat, 

)eg. 


66 Deg.l 


65|DegJ 


65^1 


)eg. 



TRAVERSE TABLE. 



sy 



o 


24 Deg. 


24iDeg.] 


24iDeg.| 


242Deg. 


(-»■ 
SI 


r- 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 
46.32 


Dep. 
21.35 


51 


46.59 


2a 74 


46.50 


20.95 


46.41 


21.15 


52 


47.50 


21.15 


47.41 


21.36 


47.32 


21.56 


47.22 


21.77 


52 


53 


48.42 


21.56 


48.32 21.77 


48.23 


21.98 


48.13 


22.19 


,53 


54 


49.33 


21.96 


49.24 22.18 


49.14 


22.39 


49.04 


22.61 


.54 


65 


50.24 


22.37 


50.15 22.59 


50.05 


22.81 


49.95 


23.03 


56 


56 


51.16 


22.78 


51.06123.00 


50.96 


23.22 


50.86 


23.44 


56 


57 


52.07 


23.18 


51.97l23.41 


51.87 


22.64 


51.76 


23.86 


57 


58 


52.9S 


23.59 


52.88 23.82 


52.73 


24.05 


52.67 


24.28 


58 


59 


53.90 


2400 


53.79 24.23 


53.69 


24.47 


53.58 


24.70 


59 


60 
61 


54.81 
55.73 


24.40 


54.7124.64 
55.62 25.05 


54.60 


24.88 


54.49 


25.12 

25.54 


60 
61 


24.81 


.55.51 


25.30 


55.40 


62 


56.64 


25.22 


56.53 25.46 


56.42 


25.71 


56.30 


26.96 


62 


63 


57.55 


25.62 


57.44 25.83 


57.33 


26.13 


57.21 


26.38 


63 


64 


58.47 


26.03 


58.35 26.29 


58.24 


26.54 


58.12 


26.79 


64 


65 


59.38 


26.44 


59-26 26.70 


59.15 


26.96 


59.03 


27.21 


65 


66 


60.29 


26.84 


60.1827.11 


60.06 


27.37 


59.94 


27.63 


66 


67 


61.21 


27.25 


61.09 27.52 


60.97 


27.78 


60.85 


28.05 


67 


68 


62.12 


37.66 


62.00 27.93 


61.88 


28.20 


61.75 


28.47 


68 


69 


63.03 


28.06 


62.91 28.34 


62.79 


28.61 


62.66 


28.89 


69 


70 
71 


63.95 


28.47 


63.8228.75 
64.74|29.16 


63.70 


29.03 


63.57 

64.48 


29.31 


70 
71 


64.86 


28.88 


64.61 


29.44 


29.72 


72 


65.78 


29.28 


65.65 29.57 


65.52 


29.86 


65.39 


30.14 


72 


73 


66.69 


29.69 


66.5629.98 


66.43 


30.27 


66.29 


30.56 


73 


74 


67.60 


30.10 


67.47 30.39 


67.34 


30.69 


67.20 


30.98 


74 


75 


68.52 


30.51 


68.38j30.80 


68.25 


31>10 


68.11 


31.40 


75 


76 


69.43 


30.91 


69.29 31.21 


69.16 


31.52 


69.02 


31.82 


76 


77 


70.34 


31.32 


70.21 


31.63 


70.07 


31.93 


69.93 


32.24| 771 


78 


71.26 


31.73 


71.12 


32.04 


70.98 


32.35 


70.84 


32.66! 781 


79 


72.17 


32.13 


72.03 


32.45 


71.89 


32.76 


71.74 


33.07 


79 


80 


73.08 


32.54 


72.94 


32.86 


72.80 


33.18 


72.65 


33.49 


80 


81 


74.00 


32.95 


73.85 


33.27 


73.71 


33.59 


73.56 


33.91 


81 


82 


74.91 


33.35 


74.76 


33.68 


74.62 


34.00 


74.47 


34.33 


82 


83 


75.82 


33.76 


75.68 


34.09 


75.53 


34.42 


75.38 


34.75 


83 


84 


76.74 


34.17 


76.59 


34.50 


76.44 


34.83 


76.28 


35.17 


84 


85 


77.65 


34.57 


77.50 


34.91 


77.35 


35.25 


77.19 


35.59 


85 


86 


78.56 


34.98 


78.41 


35.32 


78.26 


35.66 


78.10 


36.00 


86 


87 


79.48 


35.39 


79.32 


35.73 


79.17 


36.08 


79.01 


36.42 


87 


88 


80.39 


35.79 


80.24 


36.14 


80.08 


36.49 


79.92 


36.84 


88 


89 


81.31 


36.20 


81.15 


36.55 


80.99 


36.91 


80.82 


37.26 


89 


90 
91 


82.22 


36.61 


82.06 


36.96 


81.90 


37,32 


81.73 


37.63 
38.10 


90 
91 


83.13 


37.01 


82.97'37.38 


82.81 


37.74 


82.64 


92 


84.05 


37.42 


:83.88i37.79 


83.72 


38.15 


83.55 


•38.52 


92 


93 


84.96 


37.83 


84.79 38.20 


84.63 38.57 


84.46 


38.94 


93 


94 


85.87 


38.23 


185.71 38.61 


85.54 38.98 


85.37 


39.35 


94 


95 


86.79 


38.64 


86.62 39.02 


86.45139.40 


86.27 


39.77 


95 


96 


87.70 


39.05 


87. 53 139.43 


87.36139.81 


87.18 


40.19 


96 


97 


88.61 


39.45 


188.44 


39.84 


88.2740.23 


88.09 


40.61 


97 


98 


89.53 


39.86 


89.35 


40.25 


89.1840.64 


89.00 


41.03 


98 


99 


90.44 


40.27 


90.26 


40.66 


90.09;41.05 


89.91 


41.45 


99 


100 

■4-> 
CO 


91.35 
Dep. 


40.67 


91.18 


4L07 


91.00 


41.47 


90.81 


41.87 


100 

CO 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Q 


66 Deg 


65^Deg. 


65|Deg 


65] Dei., jo) 



-TRAVERSE TABLE. 




TRAVERSE TABLE. 



5-j25 Deg. 25^Deg.|;25iDeg. 253Deg. q 



.22 21 
.13 21 

.03:22 

;.9422 
.85 23 
1.75 23 
.66'24 
.57124 
.4724 
.33 25 



.55 46. 

,98 47. 
,40 47. 
,82 48. 
,24 49, 
,67! 50. 
,09 51. 
,51 i 52. 
,93 53, 
,36 54. 



Lat. Dep. I Lat. Dep. Lat.Dep. Lat.Dep 



61 55.28 25.78 

62 56.19 26.20 

63 57.10126.62 

64 58.00 27.05 



13 21.75 

03 22.18 
94122.61 
84123.03 
7423.46 
6523.89 
5524.31 
46^24.74 
36125.17 
27125.59 



65 58.91 
66|59.82 
67160.72 
68j61.63 28.74 
69 62.54129.16 
70.63.44129.08 



27.47 
27.89 
28.32 



7164, 

72|65. 
73,66. 
74'67, 
7567, 
76,68, 
7769, 
78 70, 
7971, 
80 72, 



35 30.01 

25 30.43 
1630.85 
0731.27 
97 31.70 
88;32.12 
7932.54 
69132.96 
60:33.39 
,50j33.81 

.41^34.23 
.32 34.65 
.2-2 35.08 
.13 35.50 
.04 35.92 
.9436.35 
.85136.77 
.7637.19 
1.6637.61 
.57 I 38.04 



SI '82.47 38.46 
02 83.38 38. 8S 
93 84.29 39.30 
94:85.19 39.73 
95|86. 10 40.15 

96 87.01 40.57 

97 87.9140.99 
9888.8241.42 
99l89.72!41.84 

100,90.63 42.26 

^ I Dep. I Lat. 



55.17i26.02 

56.0826.45 

56.98i26.87 

57.89127.30 

58.79 

59.69 

60.60 

61.50 

62.41 

63.31 

30.29 
30.71 
31.14 
31.57 
67.8331.99 
68.74:32.42 
69.64|32.85 
70..55i33.27 
71.45 33.70 
72.36 34.13 

73.26 34.55 
74.17 34.98 
75.07i35.41 
75.97i35.83 
76.88 36.28 



64.08 
64.99 
65.89 
66.79 
67.69 
68.60 



45.94i22, 
46.8422. 
47.74I23, 
48.64{23 
49.54123, 
50.44,24. 
51.34|24 
52.24j25 
53.14 25 
54.04|26 

54.94:26. 
'55.8426. 
156.74:27, 
i57.64'27, 
58.55:28, 
!59.45|28, 
160.35,29, 
'61.2529, 
162.16 29, 
63.05 30 



30.57; 

31.00; 

31.43 

31.86 

32.29 

32.72 



69.50133.15 
70.40 33.58 
,71.30 34.01 
72.21 34.44 



77.78 
78.69 
79.59 



36.68 
37.11 

37.54 



73.11 

74.01 
74.91 
75.82 
76.72 
77.62 
78.52 



,16 51 

.59 52 

,031 53 

.46! 54 

.89i 55 

,33! 56 ■ 

.76 57 

.20! 58 

.63 59 

.07J 60 

[50I 61 
.94: 62 
.37 63 
,80' 64 
,24i 65 
,67i 66 
Hi 67 
,54| 68 
,98' 69 
,41' 70 

'."si: 71 

.28; 72 

.71 73 

.15 74 

.58 75 

;.02 76 

1.45 77 

1.89 78 

:.32 79] 

1.76 80 



34.87 
35.30 
35.73 
36.16 
36.59 
37.02 
37.45 



80.5037.96 
81.40 38.39 

82.31^38.82 
83.2139.24 
84.1139.67 
85.02 40.10 
85.92!40.52 
86.8340.95 
87.73 41.38 
88.64 41.80 
89.54 42.23 
90.45;42.66 



79.43'37.88 
80.33 38.32 
81.23 38.75 



72.9635.19; 
73.8635:62: 
74.76 36.06 
75.66 36.49 
76.56 36.93 
77.46 37.36 
78.36 37.80 
79.26 38.23 
80.16 38.67 
81.06 39.10 



87] 



82.14 39, 
83.04 39, 
83.94 40, 
84.84 40, 
85.75 40, 
86.65 41. 
87.55 41, 
88.45 42, 
89.36 42, 
90.26 43, 



18 81. 

61 82. 
04 83. 
47 84. 
90 85, 
33 86, 
76 87, 

19 88, 

62 89, 
05i90, 



96 39.53 
86 39.97 
76 40.40 
67 40.84 
57 41,27 
47 41.71 
37 42.14 
27 42.58, 
17 43.01 
07 43.44 



Q 65 Peg. 



Dep. I Lat. Dep. Lat. Dep.! Lat 



643 Deg. 64] Peg. 1164^ Peg. iQ 



90 



TRAVERSE TABLE. 



26 Deg. 26iDeg.|26iDeg. 



Lat. Dep. Lat.'Dep.j Lat. Dep 



0.90 0.44 
1.80 0.88 
2.70 1.32 



3.60 
51 4.49 
6 5.39 
7| 6.29 
8, 7.19i 3.51 
9 8.09, 3.95 
10, 8.991 4.38 



1.75 
2.19 
2.63 
3.07 




0.89 
1.79 
2.68 
3.58 
4.47 
5.37 
6.26 
7.16 
8.05 
8.95 



9.84 
10.74 
11.63 
12.63 
13.42 
14.32 
15.21 
16.11 



21 18.87; 9.21 
2219.77 9.64 
23 20.67 10.08 
2421.57 10.52 

25 22.47 10.96 

26 23.37 11.40 

27 24.27 11.84 

28 25.17 12.27 

29 26.06:12.71 

30 26.9613.15 

31 27.86113.59 

32 28.7614.03 

33 29.66] 14. 47 
3430.5614.90 

35 31.46:15.34 

36 32.3615.78 

37 33.26116.22 

38 34.1516.6S 
39'35.05|17.10 
40!35.95| 17.53 

4r36.85a7.97l!: 
4237.75 18.41 

43 38.65 18.85!: 

44 39.5519.29 

45 40.45 19.73 I 

46 41.34 20.17j| 

47 42.24 20.60;i 

48 43.14 21.04:1 

49 44.04 21.48:: 
50:44.94 21. 92ii 




18.79 
19.69 
20.58 
121.48 
'22.37 
123.27 
24.16 
25.06 
25.96 
26.85 13.39 



4.91 9.82 
5.35 10.72 
5.80i 11.61 
6.25' 12.50 
6.69| 13.39 
7.14 14.29 
7.59 15.18 
8.03 16.07 
8.48 16.97 

8.92 17.86 

9.371 

9.82: 

10.26; 
10.71 

11.15; 

11.601 
12.051 
12.49 
12.94 



36.69 
37.59 

38.48 
; 39.38 

40.27 

41.17 
'42.06 
i 42.56 
143.85 

44.76 



^ Dep.l Lat. Dep.: Lat. 

P'64DegJ633Deg. 



13.83 
14.28 
14.72': 
15.17 
15.62 
16.06 
16.51 
16.96 
17.40 
17.85 

18.29 
18.74 
19.19 

19.63 
20.08 
20.53 
20.97 
21.42 
21.86 
22.31, 



4,95 11 
5.40' 12 
5.85 13 
6.301 14 
6.75; 15 
7.20 16 
7.65 17 
8.10 18 
8.55 19 
9.00 20 

9.45 21 
9.90 22 
10.35 23 
10.80 24 
11.25 25 
11.70 26 
12.15 27 
12.60 28 
13.05 29 
13.50, 30 

13.951 31 
14.40 32 
14.85 33 
15.30 34 
15.75 35 
16.20 36 
16.63 37 
17.10 38 
17.55 39 
18.00; 40 



I 



36.61 
37.51 

38.40 
39.29 
40.18 
41.08 
41.97 
42.86 
43.76 
44.65 



Dep. Lat. Dep. Lat 



45 41 

,90 42 

,35 43 

,80 44 

25 45 

70 46 

15, 47 

60 48 



63|Deg.l63}Peg.P 



TRAVERSE TABLE. 




n 



TRAVERSE TABLE. 



o 


27 Deg. 


27^Deg.| 


27iDeg.j 


27^ Deg. 


r-r- 


K 


Lat, 


Dep. 


Lat. 


Dep, 


Lat. 


Dep. 


Lat. 'Dep. 


~1 0.89 


0.45 


0.89 


0,46 


0.89 


0.46 


0.88' 0.47 


1 


2 1.78 


0.91 


1.7S 


0.92 


1.77 


0.92 


1.77} 0.93 


2 


3' 2.67 


1.36 


2.67 


1,37 


2.66 


1.39 


2.65 1,40 


3 


4! 3.56 


1.82 


3.56 


1.83 


3.65 


1.85 


3,54 1,86 


4 


5 4.45 


2.27 


4.45 


2.29 


4.44 


2.31 


4,42' 2,33 


5 


el 5.35 


2.72 


5.33 


2.75 


5.32 


2.77 


5,31 2.79 


6 


t 6.24 


3.18 


6.22 


3.21 


6.21 


3.23 


6.19 3.26 


7 


8 7.13 


3.63 


7.11 


3.66 


7.10 


3.69 


7.08i 3.72 


8 


9 8.02 


4.09 


8.00 


4.12 


7.98 


4.16 


7.96 4.19 


9 


10 


8.91 


4.64 


8.89 


4.68 


8.87 


4.62 


8.85! 4.66 


10 
11 


11 


9.80 4.99 


9.78 5.04 


9.76 


5.08 


9.73 


6,12 


12; 10.691 5.45 


10.67 5.49 


10.64 


5.54 


10.62 


5.69 12 


13[11.58| 5.90 


11.56 6.95 


11.53 


6.00 


11.50 


6,05 13 


1412.47; 6.36 


12.45 6.41 


12.42 


6,46 


12.39 


6.52 14 


15 13.37 6.81 113.34 


6.87 


13.31 


6.93 


13.27 


6.98 15 


1614.26 7.26 


14.22 


7.33 


14.19 


7.39 


14.16 


7.45 16 


1715.15 7.72 


15.11 


7.78 


15.08 


7.86 


15.04 


7.92: 17 


1816.04 8.17 


i 16.00 8.24 


15.97 


8.31 


15.93 


8.38! 18 


19,16.93' 8.63 


16.89 8.70 


16.85 


8.77 


16.81 


8.86 19 


2017.82 9.08 


17.78 9.16 


17.74 


9.23 


17.70 


9.31 


20 


21 18.7li 9.53 


18.671 9.62 


18.63 


9.70 


18.58 


9.78 


Ti 


2219.60 9.99 


19.56 10.07 


19.51 10.161 


19.47 


10.241 221 


23 20.4910.44 


20.4510.53 


20.40' 10.621 


20.35'l0.7ll 2S| 


24,21.38 10.90 


21.3410.99 


21.291L08 


21.24 


11.17; 24 


25'22.28 11.36 


22.23 11.45 


22.1811.54 


22.12 


11.641 25 


2623.17 11.80 


23.1111.90 


23.06112.01 


23.01 


12.11 26 


27 24.0612.26 


124.0012.36 


23.9512.47 


23.89 


12.671 27 


2824.9512.71 


24.8912.82 


24.84!l2.93 


24.78 


13.04 28 


29125.84 13.17 


,25.78 13.28 


25.7213.39i 


25.66 


13.50 29 


3026. 7313.62 
3l'27.62!l4.07 


126.6713.74 

1 

'27.5614.19 


26.61 


13.85 


26.55 


13.97 


30 


27.50 


14.31 


27.43 


14.43 


31 


32'28.5L14.53 '28.45 14.65ll28.38 14.78 


28.32 


14.90 


32 


3329.40 14.98 29.34 15.1i;;29.27 15.24 


29.20 


15.37 


33 


3430.29l5.44 30.23 15.57l30.16 15.70 


30.09 


15.83 


34 


35 31.1915.89131.1216.031131.0516.16 


30.97 


16.30 


35 


36 32.0816.34 


,32.0016.48; :31.93 16.62 


31.86 


16.76 


36 


37i32.97l6.80 


'32.8916.94 '32.8217.08 


32.74 


17.231 37 


3833.8617.25 


33.78 17.40 33.71 17.55 


33.63 


17.69 38 


39|34.75l7.71 


34.67ll7.86 134.69 18.01 


34.51 


18.16 39 


4035.64l8.16 


35.66 


18.31 135.48 18.47 


35.40 
36.28 


18.62 40 
19.091 41 


41 36.53! 18.61 


36.45 


18.77 36.37 18.93 


4237.42 


19.07 


137.34 


19.23 37.2619.39 


37.17 


19.661 42 


43 38.31 


19.52 


138,23 


19.69; 38.14 19,86 


38.05 


20.02 


43 


44'39.20 


19.98 


39.12 


20. 15' 139.03 20.32 


38.94'20.49 


44 


45 40.10 


20.43 


40.01 


20.60 


139,92:20.78 


39.82 20.95 


45 


46 40.99 


20.88 


40.89 


21.06 


l40.8021.24 


40.7121.42, 46 


47I4I.88 


21.34 


41.78 


21.52 


141.6921.70 


41.5921.88' 47 


48 42.77 


21.79 


142.67 


21.98 


i42.58la2.16 


42.48,22.36! 48 


49143.66 


22.25 


143.56 


22.44 


43.46 22.63 


43.3622.82 


49 


50 


44.65 


22.70 


44.46 


22.89 


44.35 23.09 


44.26 


2S.28 


50 


CO 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. Lat. 


Dep. 


Lat. 




63 Deg, 


62|Deg. 


|62iDeg. 


62iDeg. 



TRAVERSE TABLE. 




M 



TRAVERSE TABLE. 





5 

1 


28 Deg. 


28-iDeg. 


28^Deg.j 


283 Deg. 1 


^1 




Lat. 

0.88 


Pep. 

0.47 


Lat. Dep. 


Lat. 


Dep. 


Lat. j Dep. 


01 




0.88 


0.47 


0.88 


0.48 


0.88'i 0.48 l| 




2 


1.77 


0.94 


1.76 0.95 


1.76 


0.96 


l,75i 0.96 


2 




3 


2.65 


1.41 


2.64; 1.42 


2.64 


1.43 


2.631 1.44 


3 




; 4 


3.63 


1.88 


3.621 1.89 


3.52 


1.91 


3.51 1.92 


4 

5 




. 6 


4.41 


2.35 


4.40 2.37 


: 4.39 


2.39 


4.38! 2.40 




6 


5.30 


2.82 


5.29i 2.84 


i 5.27 


2.86 


5.261 2.89 


6 




7 


6.18 


3.29 


6.111 3.31 


: 6.16 


3.34; 


6.14 3.37 


7 




8 


7.06 


3.76 


7.05 3.79 


! 7.03 


3.82 


7.01 3.85 


8 




9 


7.96 


4.23 


7.93 4.26 


: 7.91i 4.291 


7.89 


4.33 


9 
10 




10 


8.83 


4.69 


8.81 4.73 


1 8.79 


4.77! 


8.77 


4.81 




11 


9.71 


6.16 


9.69 5.21 


1 9.67 


6.25| 


9.64 


5,29 


11 




12 


10.60 


6.63 


10.67 5.68 


10.56 


5.73 


10.52 


5,77 


12 




13 


11.48 


6.10 


11.45 6.15 


11,42' 6.20 


11.40 


6.25 


13 




14 


12.36 


6.67 


12.33 6>63 


12.30 6.68, 


12.27! 6.73 


14 




15 


13.24 


7.04 


13.21 7.10 


13.18, 7.16 


13.15; 7.21 


15 




16 


14.13 


7.51 


14.09 7.67 


14.06! 7.63 


14.03; 7.70 


16 




17 


16.01 


7.98 


14.98 8.05 


14.94| 8.11 


14.90' 8.18 


17 




18 


15.89 


8.46 


15.86 8.52 


15.82 8.59 


15.78 8.66 


18 




19 


16.78 


8.92 


16.74 8.99 


16.701 9.07 


16.66 9.14 


19 




20 
21 


17.66 


9.39 
9.86 


17.62 9.47 
18.50 9.94 


17.68! 9.54 


17.53 9.62 

I 


20 




18.54 


18.4610.02 


18.41 10.10 


21 




CJCi 


19.42 


10.33 


19.38 10.41 


19.33 10.50 


19.29 10.58 


22 




23 


20.31 


10.80 


20.26 10.89 


20.21 10.97 


20.16 11,06 


28 

2^1 




24 


21.19 


11.27 


21.14 11.36:21.09 11.46 


21.04 n.64 




,25 


22.07 


11.74 


22,02 11.83[ 21.97 11.93 


21.92 12.02 


25 




26 


22.96 


12.21 


22.90 12.31 


22.85 12.41 


22.79 12.61 


26 




27 


23.84 


12.68 


25.7812.78 


;23. 73 12.88 


23.67 12.99 


27 




;28 


24.72 


13.15 


24.66 13.25 


24.61 13.36 


24.55 13.47 


28 
29 




29 


25.61 


13.61 


26.56 13.73 


26.49 13.84 


25.43 13.95 




SO 


26.49 


14.08 


26.43 14.20 


26.36 14.31 


26.30 14.43 


30 




31 


27.37 


14.56 


27.3114.67 


27.2414.79 


27.18 14.91 


81 




32 


28.25 


15.02 


28.19 15.16 


28.1215.27 


28.06 15.39 


32 




33 


29.14 


16.49 


29.07 16.62 


129.00 15.75 


28.93 15.87 


33 




34 


30.02 


15.96 


29.95 16.09 


29.88 16.22 


29.81 16.35 


34 




35 


30.90 


16.43 


30.83 16.57 


30.7616.70 


30.6916.83 


35 




36 


31.79 


16.90 


31.71 17.04 


31.64 17.18 


31.5617.32 


36 




37 


32.67 


17.37 


32.59 17.61 


32.52 17.65 


32.44 17.80 


37 




38 


33.56 


17.84 


33.47 17.99 


33.39 18.13 


33.3213.28 


38 




39 


34.43 


18.31 


34.3518.46 


34.27 18.61 


34.19 18.76 


39 
40 




,40 


36.32 


18.78 


35.24J 18.93 


35.1519.09 


35.07 19.24 




41 


36.20 


19.26 


36.1219.41 


36.03 19.56 


35.95 19.72 


41 




42 


37.08 


19.72 


37.0019.88 


36.91 20.04 


36.82 20.20 


42 




43 


37.97 


20.19 


37.88 20.35 


37.79 20.62 


37.7020.68: 43 




44 


38.85 


20.66 


38.76 20.83 


38.67 20.99 


38.58 21.16 44 




45 


39.73 


21.13 


39.64 21.30 


39.55 21.47 


39.45 21.64 45 




46 


40.62 


21.60 


40.52 21.77 


140.43 21.95 


40.3322.13 46 




47 


41.50 


22.07 


41.4022.25 


141.30 22.43 


41.21 22.61 47 




48 


42.38 


22.53 


42.2822.72 


142.18 22.90 


42.08 23.09 48 




49 


43.26 


23.00 


43.1623.19 


I43.O6 23.38 


42.96 23.67 49 




50 


44.15 


23.47 


44.04 23.67 


I43.94 23.86 


43.84 24.06 60 




s 


Dep.' Lat. 


Dep.: Lat. 


Dep. Lat. 


Dep.' Lat. ^ 

00 




62 Deg, 


eiJDeg. 


ClxDeg. 


61i 


Deg. 


«i 



TRAVERSE TABLE 



a^ 



28iDeg.]|28f Deg.i ^ 



(-,28Deg. ||28iDeg. 



5145J 

62 45.1 
53 46.i 
54,47. 

56!48. 
56l49. 
57i60.i 

68 51. 

69 j 52.1 
6052. 




81l71.52l38.0S 
82j72.40'38.50 
83 73.28;38.97 
84.74. 17i39.44 

85 75.05l39.91 

86 7S.93l40.37 

87 76.82!40.84 

88 77.70 41.31 

89 78.58|41.78 

90 79.47i42.25! 

9i8O.35i42.72 

92 81.23143. 19 

93 82.1143.66 

94 83.00 44.13 

95 83.88144.60 

96 84.76 45.07 

97 85. 65 145. 64 

98 86.53 46.01 

99 87.41 46.48 
100 88.29;46.95 



80.16l43.07( 
81.04 43.65 
81.92.44.02 
82.80 44.49 
83.68 44.97 
84.57 45.44 
85.45 46,91 
86.33 46.39 
87.21 46.86 
88.09 47.33 



82.6114485 
83.49 46.33 
84.37|45.81 
85,25 46,28 
86.12 46.76 
87.00|47.24 
87.88 47.72 



79.78 43.77 91 

80.66 44.25 92 

8U54i44.73 93 

82.41:45.21 94 

83.29|45.69 96 

84. L7 [46.17 96 

85,0446.^ 97 

85.92 47.14 98 

86.80 47.62 99 
87.67i48.10 100 



4J Dep. Lat.; Dep. Lat. Dep. Lat. iDep.l Lat. ^j 
.2 ' . '\ - , - .S2 

P ! 62 Peg.! 61f Peg. lei^Deg. '61 j Peg. P 



96 TRAVERSE TABLE. 








5 

m' 
1 


29 Deg.| 


29iDe«;. 


29^Deg.! 


29iDeg. 


"i? 


Lat. 
0.87 


Dep.| 


Lat. Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


03 


0.48 


0.87 


0.49 


0,87 


0.49 


0,87 


0.60 


1 


2 


I.75I 0.97 


1.74 


0,98 


1.74 


0.98 


1.74 


0.99! 2 


3 


2.62 1.45 ! 2,62 


1,47 


2.61 


1.48 


2.60 


1.49 • 3 


4 


3,50i 1,94 1 3.49 


1.95 


3.48 


1.97 


3.47 


1.98 4 


5 


4.37: 2.42 1 4.36 


2.44 


4.35 


2.46 


4.34 


2.48 5 


6 


6.25! 2.91 1 6.231 2.93 


6.22 


2.95 ' 5.21 


2.98 6 


7 


6.12 3.39 6.11 


3.42 


6.09 


3.45 6.08 


3.47 7 


8 


7.OO1 3.88 1 6.98 


3.91 


6.96 


3.94 6.95 


3.97 8 


9 


7.87i 4.36 1 7.85 


4.40 


7.83 


4.43 7.81 


4.471 9 


10 
11 


8.75 


4.86 i 8.72 
5.33 9.60 


4.89 


8.70 


4.92 8.68 


4.96; 10 


9.62 


5,37 


9.57 


6.42 9.65 


5.46 11 


12 


10.50 


5.82 10.47 


5,86 


10.44 


5.91 10,42 


5.95i 12 


13 


11.37 


6.30 11.34 


6.35 


11.31 


6,40 11.29 


6.45I 13 


14 


12.24 


6.79 12.21 


6.84 


12.18 


6.89 12.16 


6.95' 14 


IS 


13.12 


7.27 13.09 


7.33 


13,06 


7.39 13.02 


7.441 15 


16 13.99 

17114.87 


7.76 13.96 


7.82 


13.93 


7.88 13.89 


7.94 16 


8.241 14.83 


8.31 


14.80 


8.37 14.76 


8.44 17 


18il5.74] 8.73! 15.70 


8.80 


15.67 


8.86 15.63 


8.931 18 


19ll6.62i 9.21i 16.58 


9.28 


16.54 


9.36 16.50 


9.43 19 


20 
21 


17.49 9.701 17.45 


9.77 


17.41 


9.85 17.36 
10.34 18.23 


9.92 20 
10.42 21 


18.3710.18; 18.32 


10.26 


18.28 


22 


19.2410.67! 19.19 10.75 


19.15 


10.83 19.10 


10.92 22 


23 20.12ill.l5j20.07;il.24 


20.02 


11.33 19.97 


11.41 23 


2420.991 11.64i 20.94 11.73 


20.89 


11.82 20.84 


11.91 24 


25J21.87 12.12; 21. 8112.22 


21.76 


12.31 21.70 


12.41 26 


26 22. 74! 12. 60! 22.6812. 70 


22.63 


12.80 22.67 


12.90 26 


27 23.61 13.09' 23.5613. 19 


23.60 


13.30 23,44 


13.40 27 


2824.49; 13.57 24.43,13.68 


24.37 


13.79 24.31 


13.89 28 


29125.36! 14.06 25.30 14.17 


25.24 


14.28 26.18 


14.39 29 


3e26.24|14.54 26,1714.66 


26.11 


14.77 26.06 


14.89! 30 


3127.1115.03 27.0515.15 


26.98 


15.27 26.91 


15.38i 31 


3227.99 15.51 27.92 15.64 


27.85 


15.76 27.78 


15.88 32 


3328,86116.00 28.79 16,12 


28.72 


16,25 28,66 


16.38 sa 


34 29,74! 16.48! 29.66 16.61 


29.59 


16.74 29.52 


16.87 34 


35 


30.61 I6.97I 30.54 17. IG 


30.46 


17.23 30.39 


17.37 36 


36 


31.49 17.45' 31.41 17.66 


31.33 


17.73 31.26 


17.86 36 


37 


32,36il7.94; 32.28 18.08 


32.20 


18.22 32.12 


18.36 37 


38 


33.24118.42 33. 15! 18.67 


33.07 


18.71 32.99 


18.86 38 


39i34.1lil8.9L34.03|19.66 


33.94 


19.20 33.86 


19.35 39 


40 34,98 19.39; 34.90|19.64 


34,81 


19.70, 34.73 

1 


19.86 40 


4i35.86i9.88i36.77l2O.03 


35,68 


20,19 35.60 


29.34 41 


42 36.73!20.36 36.64 20.52 


36,65 


20.68 3^.46 


20.84 42 


43 37,6l!20.85 37.52121.01 


37.43121. 17 37.33 


21.34 43 


44 38.48]21,33 38.39i21.50 


3S.30J21.67i 38.20 


21.83 44 


45 39.3621.82 39.26;21.99 


39,17i22,16 39.07 


22.33, 45 


46 40.23122.30 40.13'22.4S 


40.04 


22,65 39.94 


22.83 


46 


47 4I.lli22.79 41.0li22.97 


40.91 


23.14 40.81 


23.32 


47 


48 41.9823.27 41.88i2S.45 


41.78 


23.63 41.67 


23.82 


48 


49 42.86123.76 42.75!23.94 


42.65 


24.13 42.64 


24.31! 49 


6043.73 24.24 43.62i24.43 


43.52 


24.62 43.41 


24.8l| 60 


"« 


Dep.| Lat. 


Dep.! Lat. 


Dep. 


Lat. 


Dep.l 


Lat. 


CO 


Q 


161 Deg.i603Deu. 


eOfDeg.l 


60]Deg. 


Q 



TRAVERSE TABLE. 



— 29 Deg. 2935:Deg.!29^Deg. 29|Deg, 



51 44.6i;24.73 

52 45.48 25.21 

53 46.35 25.69 

54 47.23 26.1«| 

55 48.10 26.-66, 

56 48.98 27.15' 
5749.85 27.63 

58 50.73 28.12! 

59 51.6028.60 

60 52.48 29.09! 



T*-\ Lat.lDep. Lat.,Dep.j Lat.Dep. Lat. Dep. r^ 



61i53, 

6254. 

63 55. 

64 55, 

65 56, 

66 57, 

67 58. 

68 59. 

69 60. 

70 61. 



35:29.57| 
23 30.06 
10 30.54 
98 31.03 
8531.51 
72 32.00 
60 32.48! 
4732.97! 
35 33.45 
22 33.94 



44.50:24.92 
45.37 25.41 
46.2425.90 
47.11 26.39 
47.99 26.87 
48.8627.36 
49.73 27.85 
50.60 28.34 
51.48 28.83 
52.35 29.32, 

53.22;29.8li 
54.09 30.29 
54.97 30.78 
55.8431.27 
56.7131.76; 
57.58 32.25 
58.4632.74' 
59.33 33.23: 
60.20 33.71 
61.07 34,20 



44.39 25.11 
45.26'25.61 
46.1326.10 
47.0026.59 

47.87 27.08 
48.74 27.58 
49.61128.07 
50.48 28.56 
51.3529.05 
52.2229.55 



7162.10 34.421 

7262.97 34.91 

73 63.85 35.39 

74 64.72 35.88 

75 65.60 36.36" 

76 66.47 36.85, 

77 67.35'37.33 
78'68.22;37,82' 
79 69.09:38.30 
80;69.97!38.78 



81[70.8439, 
8271.7239, 
83 72.59'40, 
84: 73.47:40. 
8574.34;41. 
86j 75.22141. 
87]76.09'42. 
88,76.97:42. 
89,77.8443. 
90 78.72 43. 

9I79.59I44. 
9280.4644.1 

93 81.34 45.1 

94 82.21 !45.i 
9583.09'46.( 
96183.9646.1 
971848447.1 
S8,85.7147., 
9986.59'48.( 

100!87.46'48. 
.1 I 



39.58 
40.07; 
40.56 
4L04 



27:70.67 
7.5 71.54 
24 72,42 
72 73.29 
21 74.1641.53 
69| 75.03 42.02 
18, 75.9iJ42.51, 
66 76.78:43.00: 
isl 77.65|43.49: 
63:; 78. 52 43. 98 



61.80 34.96 
62.67 35.45 
63.54 35.95 
64.41 36.44 
65.28 36.93 
66.15 37.42 
67.02 37.92 
67.89 38.41 
68.76 38.90 
69.63 39.39 

70,5039.89 
71.37 40.38 
72.2440.87 
73,11 41.36 
73.98 41.86: 
74.85 42,35 
75.72 42.84 
76.59'43.33 
77,4643.83 
78,33'44,32 



44.28[25.; 
45,15 25,1 
46.0126.; 
46.8826.! 
47,7527.: 
48.62 27.' 
49.49|28,; 
50.3628,' 
51.22,29.; 
52.09,29.' 



52.9630,27 61 

53.8330.77 62 
54.70 31.26 63 
55.56 31.76! 64 
56.4332.25 
57.30 32,75 
58.17 33.25 
59.04 33.74 
59.9113424 
60.77:34.74 



Dep. I Lat. 
61 Deg. 



Dep. I Lat. 
602 Peg. 



Dep. I Lat. 
60.fDe£. 



81 



Dep. I Lat. ^^ 
_co 

eoiDeg.Q 



9S 



TRAVERSE TABLE. 



s 


30 Deg.| 


30^Deg.| 


30iDeg. 


30|Deg. 


GJ 


CD 
1 


Lat. 
0.87 


Dep. 
0.50 


Lat. 
0.86 


Dep. 
0.60 


Lat. 


Dep, 
0.51 


Lat. 
0.86 


Dep. 
0.51 


on 


0.86 


1 


2 


1.73 


1.00 


1.73 


1.01 


1.72 


1.02 


1.72 


1,02 


g 


3 2.60 


1.50 


2.59 


1.51 


2.68 


1.62 


2.58 


1.53 


3 


4 3.46 


2.00 


3.46 


2.02 


3.45 


2.03 


3.44 


2.05 


4 


5 


4.33 


2.50 


4.32 


2.52 


4.31 


2.64 


4.30 


2.56 


6 


6 


5.20 


3.00 


5.18 


3.02 


5.17 


3.05 


5.16 


3.07 


6 


7 


6.06 


.3.50 


6.05 


3.53 


6.03 


3.55 


6.02 


3.58 


7 


8 


6.93 


4.00 


6.91 


4.03 


6.89 


4.06; 


6.88 


4.09 


8 


9 


7.79 


4.50 


7.77 


4.63 


7.75 


4.57! 


7.73 


4.60 


9 


10 8.66 


5.00 


8.64 


6.04 


8.62 


5,08; 


8.59 


6,11 


10 


lli 9.53! 5.50 


9.50 


S.54 


9.48 


5.58: 


9.45 


6.62 


11 


12110.39 6.00 


10.37 


6.05 


10.34 


6.09 


10.31 


6.14 


12 


13ill.26: 6.50 


11.23 


6.55 


11.20 


6,60 


11.17 


6,65 


13 


1412.12| 7.00 


12.09 


7.05 


12.06 


7.11 


12.03 


7.16 


14 


1512.99! 7.50 


12.96 


7..T6 


12.92 


7.61 


12.89 


7.67 


15 


1613.86 8.00 


13.82 


8.06 


13.79 


8.12 


13.76 


8.18 


16 


17 14.72: 8.50 


14.69 8.56, i 14.65 


8.63 


14.61 


8.69 


17 


1815.59! 9.00 


15.55 9.07! 15.51 


9.14 


15.47 


9.20 


18 


19,16.45 9.50 


16.41 9.67 16.37 


9.64 


16.33 


9.71 


19 


20 17.32| 10.00 


17.28 lO.Oa 17.23 
18.14 10.58 1I8.O9 


10.15 
10.66 


17.19 

18.05 


10,23 


20 


2118.1910.50 


10,741 21 


22: 19.05' 11.00 


19.00 11.08 !18.96 


11.17 


18.91 


11.25! 22 


23! 19.92! 11.60 


19.87 11.59 '19.82 


11.67 


19.77 


11.76; 23 


24 20.78 12.00 


20.73 12.09 :20.68 


12.18 


20.63 


12.27 24 


25'21.65 12.50 


21.6012.59 21.54 


12.63|;21.49 


12.78 25 


26122.52 13.00 


22.46; 13.10 22.40 


13.20 22.34 13.29: 26 


27123.33,13.50 


23.32! 13.60 


23.26 


13.70:23.20113.80: 27 


28.24.25' 14.00 


24. 19 [14. 11 


24.13 


14.21 24.06 14.32J 26 


29125.11! 14.50 


26.05^4.61 


24.99 


14.72 24.9214.83! 29 


30 25.98| 15.00 


26.9215.11 


25.85 


15.23 25.78 15.34' 30 

:| 


3126.8515.50 


26.7816.62 


26.71 


15.73 '26.64 15.85 31 


32;27.7lil6.00 


27,6416.12 


27.57 


16.24 27.50!l6.36! SO 


33 28.5816.50 


28.51 16.62 


28.43!l6.75 28.36'l6.87 


33 


34 29.44 17.00 


29.37 17.13 


29.30117.26 29.2217.38 


34 


35'30.31 17.50 


30.23! 17.63 


3(3. 16; 17.76 30.0817.90 


35 


86 


31.18 


18.00 


31.10 


18.14:31.02 


18.27 30.9418.41 


3R 


.37 


32.04 


18.50 


31.96 


18.641 131. 88 


18.78 31.8018.92 


37 


38 


32.91 


19.00 


32.83 


19. 14| 132.74 


19.29 32.66 19.43 


.«?8 


39 


33.77 


19.60 


33.69 


19.65] i33.60 


19.79 33.52;19.94 


39 


40 


34.64 


20.00 


34.55 
35.42 


20. 15j {34.47 


20.30 
20.81 


34.38 20.45 


40 


4J 


35.51 


20.50 


20.65 


35.33 


35.2420.96 41 


42 


36.37|21.G0 


36.28 


21.16 


!38.19 


21.32 


36.10:21.47 


42 


43 


37.24J21.50 


37.14 


21.66 


37.05 


21.82 


36.95!21.99 


43 


44 


38.11 


22.00 


38.01 


22.17 


37.91 


22.33 


37.81 !22.50 


44 


45 


38.97 


22.60 


38.87 


22.67 


38.77 


22.84 


38.67123.01 


45 


46 


39.84 


23.00 


39.74 


23.17 


39.63 


23.35 


39.53 23.52 


46 


47'j40.70 


23.50 


40.60 


23.68 


40.60 


23.85 


40.39 24.03 


47 


48 41.57 


24.00 


41.46 


24.18 


41.38 


24.36 


41.25 24.54 


48 


49 42.44 


24.50 


42.33 


24.68 


42.22 


24.87 


42.1125.05 


49 


60 43.30 


25.00 


43.19 


26,19 


43.08 
Dep. 


25.38 
Lat. 


42.97 25.56 
Dep.l Lat, 


50 

U3 


m 

s 


Dep. 


Lat. 


Dep. 


Lat. 


60 Deg. 


59|Deg. 


59iDeg.l 


59lDeg. 


Q 



TRAVERSE TABLE. 



9d 



©30 Deg. 



r*i Lat. Dcp 



5r44.17 
5245.03 
5345.90 
5446.77 

55 47.63 

56 48.50 

57 49.36 

58 50.23 

59 51,10 
6051.96 



25.60 
26.00 
26.50 
27.00 
27.50 
28.00 
28.50 
29.00 
29.50 
30.00 



6152, 

62 53. 

63 54, 

64 55. 

65 56, 
6657, 

67 58. 

68 58. 

69 59. 
70,60. 
— i — 
7161, 

72 62. 

73 63. 
74:64. 
7564. 
76165. 



30.50 
31.00, 
31.50 
32.00 
32.50 
33.00: 
33.50 
34.00 
34.50 
35.00 



88 76 



9178. 
9279. 
9380. 
9481. 
95 82. 
96(83. 
97184. 
84. 



35.50 
36.00 
36.50 
37.00 
37.50 
38.00 
38.50 
39.00 
39.50 
40.00' 



40.50 
41.00 
41.60 
42.00 
42.60 
43.00 
43.50 
44.00 
44.50 
45.00 



45.50! 
46.00; 
46.50J 
47.00 j 
47.50! 
48.00| 
48.501 
49.00 
49.50| 
50.00 



Dep. Lat. 

60 Des 



SO^Deg. 



Lat. Dep. 



44.06 
44.92 
45.78 
46.65 
47.51 
48.37 
49.24 
50.10 
50.97 
51.83 



52.69 
53.56 
54.42 
55.29 
56.15 
57.01 
57.88 
58.74 
59.60 
60.47 



61.33 
62.20 
63.06 
63.92 
64.79 
65.65 
66.52 
67,38 
68.24 
69.11 



69.97 
70.83 
71.70 
72.56 
73.43 
74.29 
75.15 
76.02 
76.88 
77.75 



78.61 
79.47 
80.34 
81.20 
82.06 
82.93 
83.79 
84.66 
85.52 
86.38 



SOiDeg. 

Lat. Dep, 



.94 



45.841 
46.35| 
46.85 
47.35 
47.86 
48.36 
48.87 
49.37! 
49.87! 
50.38! 



Dep. Lat. I 
59|Deg.i 



Dep. I Lat. 

59iDeg. 



30|Deg, 



Lat. Dep 



43.83 
44.69 
45.55 
46.41 
47.27 
48.13 
48.99 
49.85 
50.70 
51.56 



52.42 
53.28 
54.14 
55.00 
55.86 
56.72 
57.58 
58.44 
59.30 
60.16 



61.02 
61.88 
62.74 
63.60 
64.46 
65.31 
66.17 
67.03 
67.89 
68.75 



69.61 
70.47 
71.33 
72.19 
73.05 
73.91 
74.77 
75.63 
76.49 
77.35 



78.21 
79.07 
79.92 
80.78 
81.64 
82.50 
83.36 
84.22 
85.08 
85.94 



26.08 
26.59 
27.10 
27.61 
28.12 
28.63 
29.14 
29.65 
30.17 
30.68 



31.19 
31.70 
32.21 

32.72 
33.23 
33.75 
34.26 
34.77 
35.28 
35.79 

36.30 
36.81 
37.32 
37.84 
38.35 
38.86 
39.37 
39.88 
40.39 
40.90 



41.41 
41.93 
42.44 
42.95 
43.46 
43.97 
44,48 
44.99 
45.51 
46.02 



46.53 
47.04 
47.55 
48.06 
48.57 
49.08 
49.60 
50.11 
50.62 
51.13 



81 

82 
83 
84 
85 
86 
87 
88 
89 
90 

91 

92 
93 
94 
95 
96 
97 
98 
99 
100 



Dep. Lat. 
oQj-Deg.p 



2"00 



TRAVERSE TABLE, 



Is 

CO 


31 Deg. 


31iDeg. 


31^ 


Deg. 


31|Deg. 


5 
on 


Lat. 


Dep. 


Lat. i Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.86 


0.61 


0.85i 0.52 


0.85 


0.62 


8.85 


0.53 


1 


2 


1.71 


1.03 


1.7l! 1.04 


1.71 


1.04 


1.70 


1.05 


2 


3 


2.67 


1.56 


2.56 1.66 


2.56 


1.67 


2.65 


1.58 


3 


4 


3.43 


2.06 


3.42; 2,08 


3^1 


2.09 


3.40 


2.10 


4 


6 


4.29 


2.58 


4.27 1 2.59 


4.26 


2.61 


4.25 


2.63 


6 


6 


5.14 


3.09 


5.13! 3.11 


5.12 


3.13 


5.10 


3.16 


6 


7 


6.00 


3.61 


5.981 3.63 


5.97 


3.66 


5.95 


-3.68 


7 


8 


6.86 


4.12 


6.84! 4.15 


6.82 


4.18 


6.80 


4.21 


8 


9 


7.71 


4.64 


7.69! 4.67 


7.67 


4.70 


7.66 


4.74 


. 9 


10 
11 


8.57 
9.43 


6.15 
6.67 


8.561 5.19 


8.53 


5.22 


8.50 


5.26 


10 


9.40 6.71 


! 9.38 


6.76 


9.35 


5.79 


U 


12 


10.29 


6.18!l0.26; 6.23 


10.23 


6.27 


10.20 


6.31 


12 


13 


11.14 


6,70 11.11 6.74 


11.08 


6.79 


111.05 


6.84 


13 


14 


12.00 


7.21 


11.97! 7.26 


11.94 


7.31 


11.90 


7.37 


14 


15 


12.86 


7.73 


12.82j 7.78 


12.79 


7.84 


12.76 


7.89 


15 


16 


13.71 


8.24 


13.68 


8.30 


13.64 


8.36 


13.61 


8.42 


16 


17 


14.57 


8.76 


14.63 


8.82 


14.49 


8.88 


14.46 


8.95 


17 


18 


15.43 


9.27 


15.39 


9.34 


: 15.35 


9.40 


15.31 


9.47 


18 


19 


16.29 


9.79 


16.24 


•9.86 


16.20 


9.93 


16.16 


10.00 


19 


20 


17.14 


10.30 


17.1010.38 
17.95110.89 


17.05 
17.91 


10.45 
10.97 


17.01 

17.86 


10.52 
11.06 


20 
21 


21 


18.00 


10.82 


22 


18.86 


11.33 


18.81111.41 


18.76 


11.49 


18.71'11.58 


22 


23 


19.71 


11.85 


19.6611.93 


!l9.61 


12.02 


19.56112.10 


23 


24 


20.57 


12.36 


20.5212.45 


!20.46 


12.54; 


20.41 12.63 


24 


25 


21.43 


12.88 


21.3712.97 21.32 


13.06; 


21.26 


13.16 


25 


26 


22.29 


13.39 22.2313.49 22.17 


13.58! 


22.11 


13.68 


26 


27 


23.14 


13.91 


23.08 14.01 23.02 


14.llll22.96 


14.21 


27 


,28 


24.00 


14.42 


23.94 14.53! 23.87 


14.631123.81 


14.73 


28 


29 


24.86 


14.94 


24.79 15.C4i 24.73 


16.15 24.66 


15.26 


29 


30 


25.71 


15.45 


25.65 15.66| 25.58 
26.50 16.08! !2€.43 


15.67 25.51 
16.20 26.36 


15.79 
16.31 


SO 
31 


31 


26.57 


15.97 


82 


27.43 


16.48 


27.3616.601:27.28 


I6.72! 27.21 


16.84 


32 


33 


28.29 


17.00 


28.21 17.12 !28. 14 


17.24 28.06 


17.37 


S3 


34 


29.14 


17.51 


29.07 17.64 28.99 


17.76 !28.91 


17.89 


34 


35 


30.00 


18.03 i29:92 18.16! 29.84 18.29 129.76 


18.42 


35 


36 


30.86 


18.54 30.78 18.68' 30.70 18.81 130.61 


18.94 


36 


37 


31.72 


19.06ll31.63 19.19 31.55 19.33 !31.46 


19.47 


37 


38 


32.57 


19.57 32.49 19.71! S2.40 19.85 ,32.31120.00 


38 


39 


33.43 


20.09! !33.34 20.23: S3.25l20.38 |33.16|20.62 


39 


40 


34.29 


20.60! 


34.2020.75 34.11 
35.05 21.27 34.96 


20.90: 


34.01 21.05 
34.86 21.57 


40 
41 


41 


35.14 


21.121 


21.42 


42 


36.00 


21.63ii35.9121.79i 35.81 


21.94: 


35.71 22.10 


42 


43 


36.86 22.15i!36.76 22.31 36.66 22.47! 


36.5722.63 


43 


44 


37.72 22.66il37.62 22.83! 37.52 22.99' 


37.42 23.15 


41 


45 


38.57 


23. 1 8': 138.47 23.34! 38.37|23.51 


38.27i23.68 


45 


46 


39.43 


23.69!i39.33 23.86 


39.22124.03 i39.12|24.21 


46 


47 


40.29 


24.211 [40.18 24.38 


40.071 


24.56; 


39.97 24.73 47 j 


48 


41.14 


24. 72||41.04 24.90 


40.93] 


25.081 


40.82'25.26 


48 


49 


42.00 


25.24 |41.89!25.42 


41.78 


25.60! 


41.67!25.78 


49 


50 


42.86 


25.75 


42.75 25.94) 


42.63 


26.12 


42.62j26.31 


60 


— 















— 


.2 


Dep. 


Lat. 


Dep. Lat. 


Dep. 


Lat. 

1 


Dep. 1 Lat. 


4.J 


59 Deg. ; 


58fDeg. 


58iDeg.| 


SSiDeg. 









TRAVERSE TABLE. 




16i 


m' 
61 


31 Deg. 


31iDeg. 


Sl^Deg. 


31gDeg. 


ES' 
51 


Lat. 

43.72 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 

26.65 


Lat. 
43.37 


Dep. 


26.27 


43.60 26.46 


43.48 


26.84 


62 


44.57 


26.78 


44.46 26.98 


44.34 


27.17 


44.22 


27.36 


62 


US 


45.43 


27.30 


45.31 i?7.49 


45.19 


27.69 


45.07 


27.89 


53 


64 


46.29 


27.81 


46.17 28.01 


46.04 


28.21 


45.92 


28.42 


64 


65 


47.14 


28.33 


47.02 28.53 


46.90 


28.74 


46.77 


28.94 


55 


56 


48.00 


28.84 


47.88 29.05 


47.75 


29.26 


47.62 


29.47 


66 


67 


48.86 


29.36 


48.73j29.67 


48.60 


29.78 


48.47 


29.99 


67 


58 


49.72 


29.87 


49.58l30.09 


49.46 


30.30 


49.32 


30.52 


68 


59 


50.57 


30.39 


50.44 30.61 


50.31 


30.83 


50.17 


31.05 


69 


60 
61 


51.43 
52.29 


30.90 


51.29131.13 

i 

62.1531.66 


51.16 


31.35 


61.02 


31.57 


60 
61 


31.42 


52.01 


31.87 


51.67 


32.10 


62 


53.14 


31.93 


53.00:32.16 


52.86 


32.39 


62.72 


32.63 


62 


63 


54.00 


32.45 


53.86'32.68 


53.72 


32.92 


63.57 


33.15 


63 


64 


54.86 


32.96 


54.71:33.20 


64.57 


33.44 


54.42 


33.68 


64 


65 


56.72 


33.48 


56.57 '33. 72 


55.42 


33.96 


56.27 


34.20 65 1 


66 


56.57 


33.99 


66.42[34.24 


56.27 


34.48 


56.12 


34.73 


66 


67 


57.43 


34.51 


67.28134.76 


67.13 


36.01 


56.98 


36.26 


67 


68 


58.29 


35.02 


58.13i35.28 


57.98 


35.53 


57.82 


36.78 


66 


69 


59.14 


35.64 


58.99135.60 


58.83 


36.05 


68.67 


36.31 


69 


70 


60.00 


36.05 


69.84 36.31 


69.68 


36.67 


59.52 


36.83 
37.36 


70 
71 


71 


60.86 


36.67 


60.70 36.83 


60.54 


37.10 


60.37 


79. 


61.72 


37.08 


61.55;37.35 


61.39 


37.62 


61.23 


37.89 


72 


73 


62.57 


37.60 


62.4137.87 


62.24 


38.14 


62.08 


38.41 


73 


74 


63.43 


38.11 


63.26J38.39 


63.10 


38.66 


62.93 


38.94 


74 


75 


64.29 


38.63 


64:l2!38.9i 


63.95 


39.19 


63.78 


39.47 


76 


76 


65.14 


39.14 


64.97'39.43 


64.!-0 


39.71 


64.63 


39.99 


76 


77 


66.00 


39.66 


66.83 


39.95 


65.65 


40.23 


65.48 


40.62 


77 


78 


66.86 


40.17 


66.68 


40.46 


66.51 


40.76 


66.33 


41.04 


78 


79 


67.72 


40.69 


67.54 


40.98 


67.36 


41.28 


67.18 


41.57 


79 


80 
81 


68.57 
69.43 


41.20 


68.39 


41.50 


68.21 


41.80 


68.03 

68.88 


42.101 801 


41.72 


69.25 


42.02 


69.06 


42.32 


42.62 


81 


8?, 


70.29 


42.23 


7040 


42.64 


69.92 


42.84 


69.73 


43.15 


82 


83 


71.14 


42.75 


70.96 


43.06 


70.77 


4S.37 


70.58 


43.68 


83 


84 


72.00 


43.26 


71.81 


43,68 


71.62 


43.89 


71.43 


44.20! 84| 


85 


72.86 


43.78 


72,67 


44.10 


72.47 


44.41 


72.28 


44.73 


85 


8fi 


73.72 


44.29 


73,52 


44.61 


73.33 


44.93 


73.13 


45.25 


86 


87 


74.57 


44.81 


74.38 


45.13 


74.18 


45.46 


73.98 


46.78 


87 


88 


75.43 


45.32 


76.23:45.65 


75.03 


45.98 


74.83 


46.31 


88 


89 


76..29 


45.84 


76.09 46.17 


75.88 


46.50 


75.68 


46.83 


89 


90 
91 


77.15 


46.35 


76.94|46.69 

1 

77.80147.21 


76.74 


47.02 


76.63 

77.38 


47.36 


90 
91 


78.00 


46.87 


77.59 


47.56 


47.89 


99. 


78.86 


47.38 


78.66l47.73 


76.44 


48.07 


78.23 


48.41 


92 


93 


79.72 


47.90 


79.61:48.26 


79.30 


48.59 


79.08 


48.94 


93 


94 


80.57 


48.41 


80.36 48.76 


80.15 


49.11 


79.93 


49.47 


94 


95 


81.43 


48.93 


f-1. 22 49.28 


81.00 


49.64 


80.78 


49.99 


95 


96 


82.29 


49.44 


82.07 49.80 


t81-85 


50.16 


81.63 


60.62 


96 


97 


83.15 


49.86 


82.93|50.32 


182.71 


50.68 


82.48 


51.04 


97 


98 


84.00 


60.47 


83. 78 150.84 


83.56 


61.20 


63.33 


51.57 


98 


99 


84.86 


60.99 


84.64|51.36 


84.41 


51.73 


84.18 


62.10 


99 


100 


85.72 
Dep. 


51.50 
Lat. 


85.49 
Dep. 


61.88 


86.26 


62.25 


86.04 


52.62 


100 

to 

P 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


59. Deg 


SS^Deg. 


58^Deg. 


58^Det;. 



102 



TRAVERSE TABLE, 



So' 

1 


32 Deg. 


32iDeg.| 


32^Deg.| 


32peg.| 


2 

ES' 
ft- 

1 


Lat. 
0.85 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat, 


Dep. 


0.53 


0.85 


0.53 


0.84 


0.54 


0.84 


0.54 


2 


1.70 


1,06 


1.69 


1.07 


1.69 


1.07 


L68 


1.08 


2 


a 


2.54 


1.59 


2.54 


1,60 


2.53 


1.61 


2.52 


1.62 


3 


4 


3.39 


2.12 


3.38 


2.13 


3.37 


2.15 


3.36 


2.16 


4 


b 


4.24 


2.65 


4.23 


2.67 


4.22 


2.69 


4.21 


2.70 


5 


6 


5.09 


3,18 


5.07 


3.20 


5.06 


3.22 


5.05 


3.25 


6 


7 


5.94 


3.71 


5.92 


3.74 


5.90 


3.76 


5.89 


3.79 


7 


« 


6.78 


4.24 


6.77 


4.27 


6.75 


4.30 


6.73 


4.33 


8 


9 


7.63 


4.77 


7.61 


4.80 


7.59 


4.84 


7.57 


4.87 


9 


10 
11 


8.48 


5.30 


8.46 


5.34 


8.43 


6.37 


8,41 


5.41 


10 
11 


9.33 


6.83 


9.30 


5.87 


9.28 


5.91 


9.25 


5.95 


12 


10.18 


6.36 


10.15 


6.40 


10.12 


G.45 


10.09 


6.49 


12 


la 


11.02 


6.89 


10.93 


6.94 


10.96 


6.98 


10.93 


7.03 


13 


14 


11.87 


7,42 


11,84 


7.47 


11.81 


7,52 


11.77 


7.57 


14 


16 


12,72 


7.95 


12.69 


8,00 


12.65 


8.06 


12.62 


8,11 


15 


16 


13.57 


8.48 


13.53 


8.54 


13.49 


8.60 


13.46 


8.6S 


16 


17 


14.42 


9.01 


14.38 


9.07 


14.34 


9.13 


14.30 


9.20 


17 


18 


15.26 


9.54 


15.22 


9.61 


15.18 


9.67 


15.14 


9.741 181 


19 


16.11 


10.07 


16.07 


10.14 


16.02 


10.21 


15.98 


10.28i 19 1 


20 
21 


16.96 
17.81 


10.60 


16.91 


10.67 


16.87 


10.75 


16.82 


10.82 


20 
21 


11.13 


17.76 


11,21 


17.71 


11.28 


17.66 


11.36 


22 


18.66 


11.66 


18.61 


11.74 


18.56 


11.82 


18.50 


11.90 221 


23 


19.51 


12.19 


19.45 


12.27 


19.40 


12.36 


19,34 


12.44 23| 


24 


20.35 


12.72 


20.30 


12.81 


20.24 


12.90 


20.18 


12.98 24| 


26 


21.20 


13.25 


21.14 


13.34 


21.08 


13.43 


21.03 


13.52 


25 


26 


22.05 


13.78 


21.99 


13.87 


21.93 


13.97 


21.8V 


14.07 


26 


27 


22.90 


14.31 


22.83 


14.41 


22.77 


14.51 


22.71 


14.61 


27 


28 


23.75 


14.84 


23.68 


14.94 


23.61 


15.04 


23.55 


15.15 


28 


29 


24.59 


15.37 


24.53 


15.47 


24.46 


15.58 


24.39 


15.69 


29 


30 
31 


25.44 


15.90 


25.37 


16.01 


25.30 


16.12 


25.23 


16,23 


30 


26.29 


16.43 


26.22 


16.54 


26.15 


16.66 


26.07 


16.77 


31 


32 27.14 


16.96 


27.06 


17.08 


26.9S 


17.19 


26.91 


17.31 


32 


3327.99 


17.49 


27.91 


17.61 


27.83 


17.73 


27.75 


17.85 33| 


34:28.83 


18.02 


28.76 


18.14 


28.68 


18.27 


28.60 


18,39 


34 


3529.68 


18.55 


29.60 


18.68 


29.52 


18.81 


29.44 


18.93 


35 


36I30.3S 


19.08 


30.46 


19.21 


30.36 


19.34 


30.28 


19.48 


36 


37131.38 


19.61 


31.29 


19.74 


31.21 


19.88 


31.12 


?,0.02 


37 


38J32.23 


20.14 


32.14 


20.28 


32.05 


20.42 


31.96 


20.56 


38 


39i33.07 


20.67 32.98 


20.81 


32.89 


20.95 


32.80 


21.10 


39 


40 


33.92 


21.20 


33.83 
34.67 


21.34 


33.74 


21.49 


33.64 


21.64 


40 
41 


41 


34.77 


21.73 


21.88 


34,58 


22.03 


34.48 


22.18 


42 35.62 


22.26 


35.52 


22.41 


35,42 


22.57 


35.32 '22. 72 


42 


43 36.47 


22.79 


36.37 


22,95 


36.27 


23,10 


36.16i23.26 


43 


4437.31 


23.32 


37,21 


23,48 


37.11 


23.64 


37.01 J23.80 


44 


46 38.16 


23.85 


38.06 


24,01 


37.96 


24.18 


37.85 24.34 


45 


46 39.01 


24.38 


38.9C 


24.55 


38.80 


24.72 


38.69 24.88 


46 


47 39.86 


24.91 


39.75 


26.08 


39.64 


25.25 


39.63 25.43 


47 


48:40.71 


25,44 


40,59 


25.61 


40,48 


25.79 


40.37l25.97 


48 


49|41.55 


25,97 


41.4-3 


26.15 


41.33 


26.33 


41.31126.51 


49 


60 


42.40 


26.50 


42,29 


26.68 


42.17 


26.86 


42.05i27.05 


50 

CO 

Q 


Dfep. 


Lat. 


Dep. 


Lat, 


Dep, 


Lat, 


Dep. 


Lat. 


P 58 De-. 


i573Deg. 


57^Deg. 


ST^Deg. 



TRAVERSE TABLE. 




104 



TRAVERSE TABLE. 





33 Deg. 


33iDeg. 


33peg. 


33|Deg. 



I 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 

0.83 


Dep. 

65 


Lat. 


Dep. 


1 


0.84 


0.54 


0.84 


0.55 


0.83 


0.56 


2 


1.68 


1.09 


1.67 


1.10 


h67 


1.10 


1.66 


1.11 


2 


S 


2,52 


1.63 


2.51 


1,64 


2.50 


1.66 


2.49 


1.67 


3 


4 


3.35 


2.18 


3.35 


2.19 


3.34 


2.21 


3.33 


2.22 


4 


5 


4.19 


2.72 


4.18 


2.74 


4.17 


2.76 


4.16 


2.78 


6 


6 


5.03 


3.27 


5.02 


3.29 


5.00 


3.31 


4.99 


3,33 


6 


7 


5.87 


3.81 


5.85 


3.84 


5.84 


3.86 


5.82 


3.89 


7 


8 


6.71 


4.3S 


6.69 


4.39 


6.67 


4.42 


6.65 


4.44 


8 


9 


7.55 


4.90 


7.53 


4.93 


7.50 


4.97 


7.48 


5.00 


9 


10 


8.39 


5.45 


8.36 


5.48 


8.34 


5.52 


8.31 


5.56 


10 


11 


9.23 


5.99 


9.20 


6.03 


9.17 


6.07 


9.15 


6.11 


11 


1210.06 


6.54 10.04 


6.58 


10.01 


6.62 


9.98 


6.67 


12 


1310.90 


7.08 10.87 


7.13 


10.84 


7.18 


10.81 


7.22 


13 


1411.74 


7.62 


11.71 


7.68 


11.67 


7.73 


11.64 


7.781 14| 


15 12.58 


8.17 


12.54 


8.22 


12.51 


8.28 


12.47 


8.33 


15 


16 13.42 


8.71 


13.38 


8.77 


13.34 


8,83 


113.30 


8.89 


16 


1714.26 


9.2« 


14.22 


9.32 


14.18 


9.38 


I14.I3 


9.44 


17 


1815.10 


9.80 


16.05 


9.87 


15.01 


9.93 


14.97 


10.00: 181 


19 15.93 


10.35 


15.89 


10.42 


15.84 


10.49 


15.80 


10.56i 19| 


20|16.77 


10.89 


16.73 


10.97 


16.68 


11.04 


[16.63 


11.11 


20 
21 


21:17.61 


11.44 


17.56 


11.51 


17.51 


11.59 


17.46 


11.67 


22! 18.45 


11.98;'18.40'12.06 


18.35 


12.14 


il8.29 


12.22 


22 


23119.29 


12.53! 19.23 12.61 


19.18 


12.69 


il9.12 


12,78| 23 


24 20.13 


13.07! 20.07 13.16 


20.01 


13.26 


19.96 


13.33 24 


^ 20.97 


13.62;!20.9ri3.71 


20.85 


13.80 


:20.79 


13.89 25 


26 21.81 


14.16! 21.74 14.261 


21.68 


14.36 


21.62 


14.44! 26 


27 22.64!l4.71i[22.5814.80| 


22.51 


14.90 


;22.45 


15.00 


27 


28,23.48 15.25' 23.42 15.351 


23.35 


15.45 


23.28 


15.56 


28 


29 24.32 15.79,24.25 15.90| 


24.18 


16.01 


24.11 


16.11 


29 


80 25.16 16.34 25.09 16.45 


25.02 


16.56 


24.94 

25.78 


16.67 


30 


31 26.00 16.88 '25.92 n.OO' 


25.85 


17.11 


17.22: 31 


32!26.84 17.43i;26.76 17.55' 


26.68 


17.66 


26.61 


17.78: 32 


SS 27.68:17.97 '27.60 18.09 


27.52 


18.21 


27.44 


18.33 33 


34 28.51,18.52! 28.43 18.64 


28.35 


18.77 


28.27 


18.89 34 


35!29,35; 19.06 29.27 19.19 


29.19 


19.32 


29.-10 


19.44 35 


36 30.19 19.61' 30.11 19.74 


30.02 


19.87 


29.93 


20.00 36 


37!31.03|20.15':30.94 20.29 30.86 


20.42 


30.76 


20.56; 37 


38:31.87:20.70!'31.78 20.84l;31.69 


20.97 


31.60 


21.11 38 


39:32.7l'21.24; 32.62 21.38' 32.52 


21.53 


32.43 


21.67 39 


40!33.55'21,79! 33.45 21.93' 33.36 

1 1 li , |l 


22.08 


33.26 


22.22 40 


4l'34.39!22.33!!34.29;22.48l;S4.19 


22.63 


34.09 


22.78 41 


42'35.22|22.87:l35.12:23.03 


35.02 


23.18i'34.92 


23.33 42 


43,36.06 


23.42' 135.96:23.58 


35.86 


23,73; 35.75 


23.89 43 


4436.90 


23.96' 36.80 24. 12 


36.69 


24.29 36.58 


24.45 44 


45!37.74 


24.51|'37.63 24.67 


37.52 


24.84 


37.42 


25.00 


45 


46:38.58 


25.05 


38.4725.22 


38.36 


25.39 


38.25 


25.56 


46 


47:39.42 


25.60 


39.31:25.77 


39.19 


25.94 


39.08 


26.11 


47 


48,40.26 


26.14 


40.14 26.32 


40.03 


26.49 


39.91 


26.67 


48 


49',41.09 


26.69 


40.98 26.87 


'40.86 


27.04 


40.74 


27.22 


49 


60 


41.93 27.23 


41.8127.41 


41.69 


27.60 


41.57 


27.78J 601 


1^ 


Dep.l Lat. 


Dep. Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


00 


67 Deg. 


56fDeg. 


66iDeg. 


l56iDeg. 


Q 



TRAVERSE TABLE. 



105 



7159. 

72 60. 

73 61. 
74,62, 
76 62. 
76 63, 
77'64. 
78i65, 

79 66, 

80 67, 



55 38.67 
38 39.21 
22 39.76 
06 40.30 
90 40.85 
74 41.39 
58 41.94 
,42 42.48 
,25 43.03 
.09 43.57 



8167.93 44.12 

82 68.77 44. 

83 69.61 45.20 

84 70.45 43.75 

85 71.29 46.29 

86 72.13 46.84 



87 72.96 

88 73.80 

89 74.64 
90; 75.48 



47.38 
47.93 
48.47 
49.02 



33iDeg. 33|Deg.| Q 




59.38 38.93 
60.21 39.48 
61.05 40.03 
61.89 40.57 
62.72 41.12! 
63.56 41.67 

64.39 42.22 
65.23 42.77 
66.07 43.32 
66.9043.86 



59.2139.19 
60.04 39.74 

60.87 40.29 
61.7140.64 
62.54 41.40 
63.38 41.95 
64.21 42.60 
65.04 43.05 

65.88 43.60 
66.7144.15 



59.03 39.45 71 

59.87 4O.0OJ 72 

60.70 40.56 73 

61.63 41.111 74 

62.36 41.671 75 

63.19 42.22! 76 

64.02 42.78| 77 

64,86 43.331 78 

65.69 43.89| 79 
66.52 44.45 




8350.00 90 



9l!76.32 49.56 
92; 77. 16 50.11 

93,78.00!50.65 
94|78.83 51.20 
95,79.67 51.74 



9680.51 
9781.35 
98182.19 
99,83.03 
100 83.87 



52.29 
52.83 
53.37 
53.92 
54.46 



76.1049.89! 
76.94 50.44 
77.77 50.99 
78.61 61.64 
79.45 62.09 
80.28 52.64 
81.12 63.18 
81.96 53.73 
'82.79 54.28 
183.63 54.831 



75,8850.23 
76.7250.78 
77.55 51.33 
78.3951.88 
79.22 52.43 
80.05 52.99 
80.89 53.54! 
81.72 54.09 
82.55 54.64, 
i83.39 56,19 



75.66 50. 
76.50 51, 
77.3351, 
78.16,52, 
78.99 52, 
79.82153, 
80.65153, 
81.48 54. 
82.32 55, 
83,15 55. 



Dep. Lsit. 



Dep. Lat. Dep.i Lat. 



Dep. I Lat. 



Q 57 Peg 



56jDeg. 56»Deg. 

20 ' 



56j^Deg. 



IQ^ 



TRAVERSE TABLE. 



P. 

en 
«-^ 

1 


34 Deg.| 


34iDeg. ^ 


34^Deg. 


343Ueg.| 


5 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 




0.83 


0.56 


0.83 


0.56 


0.32 


0.57 


0.82 


0.57 l| 


3 


1.66 


1.12 


1.65 


L13 


1.65 


1.13 


1.64 


L14 


2 


3 


2.49 


1.68 


2.48 


L69 


2.47 


1.70 


2.46 


L71 


3 


4 


3.32 


2.24 


3.31 


2.25 


3.30 


2.27 


3,29; 2.28 


4 


5 


4.15 


2.80 


4.13 


2.81 


4.12 


2.83 


4.III 2.85 


6 


6 


4.97 


3.36 


4.96 


3.38 


4.94 


3.40 


4.93| 3.42 


6 


7 


5.80 


3.91 


6.79 


3.94 


5.77 


3.96 


6.75' 3.99 


7 


8 


6.63 


4.47 


6.61 


4.50 


6.59 


4.53 


6.57 4.56 


8 


9 


7.46 


6.03 


7.44 


6.07 


7.42 


5.10 


7.39 5.13 


9 


10 


8.29 


5.69 


8.27 


5.63 


8.24 


6.66 


8.22 5.70 


10 


,11 
12 


9.12' 6.15 


9.09 


6.19 


9.07 


6.23 


9.04' 6.27 


11 


9.95 6.71 


9.92 


6.75 


9.89 


6.80 


9.86 6.84 


12 


1310.78i 7.27 


10.76 


7.32 


10.71 


7,36 


10.68 7.41 


13 


1411.61' 7.83 


11.67 


7.88 


n.54 


7.93 


11.60 7.98 


14 


1512.44 8.39 


12.40 


8.44 


12.36 


8.50 


12.32 8.55 


15 


1613.26; 8.95 


13.23 


9.00 


13.19 


9.06 


13.15 9.12 


16 


i7jl4.09l 9.51 


14.05 


9.57 


14.01 


9.63 


13.97 9.69 


17 


1814.92 10.07 


14.88 


10.13 


14.83 


10.20 


14.79 10.26 


18 


19:15.7510.62 


16.71 


10.69 


15.66il0.76 


15.61 10.83 


19 


20' 16.58 11,18 
,2l'l7.4111.74 


16.53 


11.26 
11.82 


16.4811.33 
17.31|11.89 


16.43 11.40 
17.25 11.97 


20 
21 


17.36 


'22 18.24' 12.30 


18.18 


12.38 


18.1312.46 


18.08 12.54! 22 


2319.0712.86 


19.0lil2.94 


18.9613.03 


18.9013.11 


23 


2419.9013.42 


19.8413.61 


19.78 13.59 


19.72 13.68 


24 


25 20.73 13.98 


20.6614.07 


20.6014.16 


20.54 14.25 


25 


26 21.55 14.64 


21.49 14.63 


21.4314.73 


21.36 14.82 


26 


27,22.3815.10 


22.32 15.20 


22.25 15.29 


22.18 15.39 


27 


28'23.2115.66 


23.1416.76 


23.08 16.86 


23.01 15.96 


28 


29|24.04 16.22 


23.97 16.32 


23.90!l6.43 


23.83 16.53 


29 


30,24.8716.78 


24.8O! 16.88 


24.7216.99 


24.65 17.10 


30 


3l26.70'l7.33 


26.62|l7.45 


25.55! 17.56 


25.47 17.67 


31 


32 26.63l7.89 


26.4518.01 


26.3718.12 


26.29 18.24 


32 


33 27.36i 18.45 


i27.2818.67 


27.2018.69 


27.1118.81 


33 


34J28. 19 19.01 


28.10|19.14 


28.02 19.26 


27.94 19.38 


34 


35j29.02 19.67 


28.9319.70 


28.84 19.82 


28.76 19-95 


35 


36 29.85,20.13 

37 30.67 20.69 


129.7620.26 


29.67 20.39 


29.68 20.52 


36 


30.6820.82 


30.49 20.96 


30.40 21.09 


37 


38|31.50,21.25i 31.41 21.39 


31.32 21.52 


31.22 21.66! 38 


39|32.33 21.81 


32.24:21.95 


32.14 22.09 


32.04 22.23I 39 


.4C 


33.16 22.37 


33.06|22.51 


32.97 22.66 


132.87 22.80| 40 


41 


33.99122.93 


33.89 23.07 


33.79 23.22 


133.69 23.37! 41 


45 


34.82 23.49; 34.7223.64 


34.61 23.79 


j34.51 23.94! 42 


4£ 


35.65 24.05 35.64 24.20 


35.44 24.36 


'35.33 24.51' 43 


44 36.48 24.60! 36.37 24.76 


36.26 24.92 


!36. 15 25.08' 44 


46 37.31 25.161:37.20 25.33 


37.09 25.49 


36.97 25.65 45 


46 38. 1425.721 '38.02 25.89 


37.91 26.05 


137.80 26.22 46 


47|38.96 26.28' 38.85 26.45 


38.7326.62 


i38.62 26.79; 47 


,45 


S 39.79 26.84! ,39.68 27.01 


39.56 27.19 


39.44 27.36 48 


4£ 


40.62l27.40 


140.50 27.58 


40.38 27.75 


40.2627.93 49 


6( 


) 41.45 27.96 
Dep. Lat. 


41.3328.14 

1 


41.21 28.32 


41.08 28.60 


50 


Dep.! Lat. 


Dep. Lat. 


Dep. Lat. 


CO 

S., 


56 Deg. 


553De;.^ 


55i|Deg. 


55,iDeg. 



TRAVERSE TABLE. 



10^ 



'34 Deg. j34|Deg. 



Lat. Dep. | Lat. Dep 



5142.28 
62:43.11 
63;43,94 
54,44.77 
65 45.60 
56146.43 
57;47.26 
58;48.08 
59i48.91 
60 49.74 



6150.57 
6251.40 

63 52.23 

64 53.06 
65i53.89 
66 54.72 
67,55.56 
68 56.37 
6957.20 
70; 58.03 

7158.86 



28.52 
29.08 
29.64 
30.20 
30.76 
31.31 
31.87 
32.43 
32.99 
33.55 



34.11 

34.67 
35.23 
35.79 
36.35 
36.91 
37.46 
38.03 
38.58, 
39.14 

39.70 



40.26 
40.82 
41.38 



72 59.69 

73 60; 52 

74 61,35 

75 62.18 41.94 

76 63.0142.50 

77 63.84143.06 

78 64.66143.62 

79 65.49144. 18 

80 66.32l44.74 



91 75.4450.89 

92 76.27 51.45 

93 77.10 52.00 

94 77.93 52.56 

95 78.76 53.12 

96 79.59 53.68 

97 80.42 54.24 

98 81.25 54.80 

99 82.07 55.36 
100 82.90 55.92 



2 . 




Uep.i Lat. Dep. I Lat.| Dep. Lat. Dep. Lat 



Q 56 Peg. 553Deg. 55jDeg.ll55|Deg.p 



108 



TRAVERSE TABLE. 



2 

GO 


35 Deg. 


35iDeg. 


35|Deg.| 


3531^ 


Ed 




Lat. 


Dep, 


Lat. 


Dep. 


Lat. 


Dep, 


Lat. 


Dep. 




1 


0.82 


0.57 


0.82 


0.58 


0.81 


0.58 


0.81 


ase 


1 




2 


1.64 


1.15 


1.63 


1.15 


1.63 


1.16 


1.62 


L17 


2 




3 


2.46 


1.72 


2.45 


1.73 


2.44 


1.74 


2.43 


1.75 


3 




4 


3.28 


2.29 


3.27 


2.31 


3.26 


2.32 


3.26 


2.34 


4 




5 


4.10 


2.87 


4.08 


2.89 


4.07 


2.90 


4.06 


2.92 


6 




6 


4.91 


3.44 


4.90 


3.46 


j 4.88 


3.48 


4.87 


3.51 


6 




7 


5.73 


4.01 


5.72 


4.04 


1 5.70 


4.06 


5.68 


4.0S 


7 




8 


6.55 


4.59 


6.53 


4.62 


6,51 


4.65 


6.49 


4.67 


8 




9 


7.37 


5.16 


7.35 


5.19 


1 7.33 


5.23 


7.30 


6.26 


9 




lOj 8.19 
11 9.01 


5.74 
6.31 


8.17 


5.77 


8,14j 5.81 


8.12 


5.84 


10 




8.98 


6.36 


' 8.96 6.39 


8.931 6.4S 


11 




12 9.83 


6.88 


9.80 


6.93 


! 9.77 6,97 


9.74; 7.01 


12 




1310.65 


7,46 


10.62 


7.50 


10,68! 7.65 


10.65; 7.6t 


13 




1411.47 


8.03 


111.43 


8.08 


11.40; 8.13 


11.361 8.U 


14 




15:12.29 


8,60 


! 12,25 


8.66 


12.211 8.71 


12.17 


8.76 


> 16 




1613.11 


9,18 


13.071 9,23 


13.03! 9.29 


12.99 


9.3t 


16 




17 


13.93 


9.75 


13,88! 9,81 


13.84 9.87 


13.80 


9.9f 


17 




18 


14.7410.32 


14.70 10.39 


14,6510.45 


14.61 


10.55 


- 18 




19 


15.56! 10.90 


15,5210.97 


15.47 11.03 il6.42 


ll.K 


> 19 




20 16.38 11.47 


il6.33;il.54 


!16.28|lL61,!l6.23 


11,66 


20 




2i 17.20 12.05 


'l7.1512.12 


17.1012.19! 17.04 


12.2' 


21 




22118.0212.62 


17.9712.70 


17.91 12.78, 17.85 


12. 8£ 


22 




2318.8413.19 


118.7813.27 


18.7213,36118.67 


13,44 


23 




2419.6613.77 


19.6013.85 


19,54 13,94! 19,48 


14.0S 


24 




25 20.481 14,34 


20.42 14.43 


20.35 14.52 j20.29 


14.6] 


26 




26 21,30: 14.91 


21.2315.01 


21.17 15.10 21.10 


15. IS 


26 




27 22.12 15.49 


22.0515.58 


21.98 15.68^21.91 


15.7- 


27 




28 22.94 16.06 


22.8716.16 


22.80il6.26 22.72 


16.36 


28 




29 23,7616.63 


i23,68 16.74 


23.6116.84 23.64 


16.94 


I 29 




30 


24,5717,21 


24.6017.31, 


,24.42 17.42 124.35 


17.6f: 


30 




31 


25.391 17.78 


25,3217.89 


25.24il8.G0' 26.16 


18.11 


31 




3226.2118.35 


26.1318.47 


!26.05'18.58 25.97 


18. 7C 


>| 32 




33 27.0318,93 


26.95 19.05 


!26.87'19.16 26.78 


19.28 


i S3 




34 27,8519.50 


27.77 19.62 


127.6819.74 27.59 


19.86 


►1 34 




35,28.67 20.08 


28.58 20.20 


128.49^20.32 !28.41 


20.45 


36 




36129.49 20.65 


29.40 20.78 


129,31 i20.91!29,22 


21.03 


36 




37130.31 


21.22 


30.22 21.35 


30.1221.49 !30.03!21.62 


37 




38 31.13 


21.80 


31.03 21.93 


30.94l22.07ii30.84,22.2C 


38 




39 


31,95 


22,37 


31.85 22.61 


31.75 


22.66H31.65 22.79 


39 




40 
41 


32,77 
33,69 


22.94 
23.62 


32.67 23,09 
33.48 23.66 


32.66 


23.231 i32.46i23.37 

'.'. .ii. ,„| 


40 




33.38 


23.81 !33.27!23.9S 


41 




42 34,40 


24.09 


34.30 24.24 


34.19 24.39.34.09,24.54 


42 




43 35,22 


24.66 


35.12 24.82 


35.0124.97 34.90 25.12 


43 




44 36,04'25.24 


35.93 25.39 


36.82 25.55 135.71 25.71 


44 




45 36.86^25.81 


36.75 25.97 


36.64I26.13136.52 26.29 


46 




46'37.68 26.38 


37.57 26.65 


37.45!26.7i:i37.33 26.88 


46 




47i38.S0|26.96 


38.38 27.13 


38.26 27.291 i38.14.27.46 


47 




48i39.32 27.53 


39.2027.70 


39.08 


27.87i 


38.96|28.04 


48 




49 40.14 28.11 


40.02 28.28 


39.89 


28.46 


39w7i28.63 


49 




66 


40.96 
Dep. 


28.68 


40.8328.86 


40.71 


29»04| 


40.58j29,21 


60 




Lat. 


Dep. Lat. 


Def>. 


Lat.l 


Dep.! Lat. 


^ 




55 DegJ'543Deg.' 


54|I 


)eg.'^54iDeg. 


a 





TRAVERSE TABLE. 



109 



P. 


35 Deg. 


35peg. 


35iDeg. 


35|Deg. 




09 
51 


Lat. 
41.78 


Dep. 

29.25 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


41.65 


29.43 


41.52 


29.62 


41.39 


29,80 


51 


52 


42,60 


29.83 


42.47 


30.01 


42.33 


30.20 


42.20 


30,3E 


52 


53 


43.42 


30.40 


43.28 


30.59 


43.15 


30.78 


43.01 


30.97 


63 


54 


44.23 


30.97 


44.10 


31.17 


43.96 


31.36 


43.82 


31,55 


54 


55 


45.05 


31.55 


44.92 


31.74 


4478 


31.94 


44.64 


32,12 


55 


56 


45.87 


32.12 


45.73132.32 


45.59 


32.52 


45.45 


32,72 


66 


57 


46.69 


32.69 


46.55132.90 


46.40 


33.10 


146.26 


33,30 


67 


5fi 


47.51 


33.27 


47.37 


33.47 


47.22 


33.68 


147.07 


33,89 


68 


59 


48.33 


33.84 


48.18 


34.05 


48.03 


34.26 


;47.88 


34,47 


69 


60 
61 


49.15 


34.41 


49.00 


34.63 


48.85 


34,84 


48.69 


35,05 


60 
61 


49.97 


34.99 


49.82 


35.21 


49.66 


35,42 


49.51 


35,64 


62 


50.79 


35.56 


50.63:35.78 


50.48|36.00'i60.32 


36,22 


62 


63 


51.61 


36.14 


51.45:36.36 


51.29 36.53 |51.13 


36.8] 


63 


64 


52.43 


36.71 


52.27'36.94 


52.1037.16Sl5I.94 


37.39 


64 


65 


53,24 


37.28 


53.0837.61 


52.9237.75 52.75 


37.98 


65 


66 


54.06 


37.36 


53.90;38.09 


53.73,38.33':53.56 


38.56 


66 


67 


54.88 


38.43 


54.71 


38.67 


5455!38.9ljl5438 


39.14 


67 


68 


55.70 


39.00 


55.53 


39.25 


55.36|39.49|l55.19 


39.73 


68 


69 


56.52 


39.58 


56.35 


39.82 


56.17 


40,07 '56.00 


40.31 


69 


70 


57.34 


40.15 


57.16 


40.40 


56.99 


40,65 


56.81 


40.90 


70 
71 


71 


58.16 


40.72 


57.98 


40.98 


57.80 


41,23 


57.62 


41.48 


72 


58.98 


41.30 


58.80 


41.55 


58.02 


41,81 


58.43 


42.07 


72 


73 


59.80 


41.87 


59.61 


42.13 


59.43 


42,39 


69.24|42.65 


73 


74 


60.62 


42.44 


60.43 


42.71 


60.24 


42,97 


60.06 


43.23 


74 


75 


61.44 


•43.02 


61.25 


43.29 


61.06 


43,55 


60.87 


43.82 


75 


76 


62.26 


43.59 


62.06 


43.86 


61.87 


44,13 


61.68 


44.40 


76 


77 


63.07 


44.17 


62.88 


44.44 


62.69 


4471 


62.49 


44.9E 


77 


78 


63.89 


44.74 


63.70 


45.02 


63.50 


45.29! ;63.30 


45.57 


78 


79 


64.71 


45.31 


64.51 


45.59 


64.32 


45.83 


6411 


46.16 


79 


80 


65.53 


45.89 


65.33 


46.17 


65.13 


46.46 


64.93 


46.74 


80 


81 


66.35 


46.46 


66.15 


46,75 


65.94 


47.04 


65.74 


47.32 


81 


82 


67.17 


47.03 


66.96 


47.33 


66,76 


47.62 166.55 


47.91 


82 


83 


67.99 


47.61 


67.78 


47.90 


67.57 


48.20 167.36 


48.49 


8.? 


84 


68.81 


48.18 


68.60 


48.48 


68.39 


48.78 68.17 


49.08 


84 


85 


69.63 


48.75 


69.41 


49.06 


69.20149.36 68.98 


49.66 


85 


86 


70.45 


49.33 


70.23 


49.63 


70.01 49.94 


69.80 


50.25 


86 


87 


71.27 


49.90 


71.05 


50.21 


70.83 50.52 


70.61 


60.83 


87 


«8 


72.09 


50.47 


71.86 


50.79 


71.64 51.10 


71,42 


51.41 


88 


89 


72.90 


51.05 


72.68 


61.37 


72.46 51.68 


72.23 


62,00 


89 


90 
91 


73.72 
74.54 


51.62 

52.20 


73.50 


51.94 


73.27 52.26 


73.04 


52,58 


90 


74.31 


52.52 


74.03 52.84 


73.85 


53,17 


91 


92 


75.36 


52.77 


75.13 


53.10 


7490'53.42 


7466 


53,75 


92 


93 


76.18 


53.34 


75.95 


53.67 


75.715401 


75.48 


54.34 


93 


94 


77.00 


53.92 


76.76 


54.25 


76.535459 


76.29 


54.92 


94 


95 


77.32 


54.49 


77.58 


54.83 


77.3455.17 


77.10 


55.50 


95 


S6 


78.64 


55.06 


78.40 


55.41 


78.16 55.75 


77.91 


56.09 


96 


97 


79.46 


55.64 


79.21 


55.98 


78.97 


56.33 


78.72 


56.67 


97 


98 


80.28 


56.21 


80.03 


56.56 


79.78 


56.91 


79.53 57.26 


98 


99 


81.10 


56.78 


80.85 


57.14 


80.60 


57.49 


80.35 57.84 


99 


iOO 

• 

Q 


81.92 
Dep, 


57.36 


81.66 
Dep. 


57.71 


81.41 
Dep. 


58.07 


81.16 58.42 


100 

wmam 


Lat. 


Lat. 


Lat. 


Dep.l 


Lat, 

)eg. 


55 Deg. 


542Deg. 


54^Deg. 


5411 



19 



110 



TRAVERSE TABLE. 



q 
1 


36 Deg.aeiDeg. 


Se^Deg. 


36 J Deg. 


5 

55 
T 


Lat, 
0.81 


Dep. 

0.59 


Lat, 
0.81 


Dep. 

0.59 


Lat. 
0.80 


Dep. 
0.59 


Lat. 


Dep, 


0.80 


0.60 


2 


1.62 


1.18 


1.61 


1.18 


1.61 


1.19 


1.60 


1.20 


'f. 


a 


2,43 


1.76 


2.42 


1.77 


2,41 


1.78 


2.40 


1.79 


3 


4 


3,24 


2.35 


3.23 


2.37 


3.22 


2.38 


3.20 


2.39 


ft 


5 


4.05 2,94 


4.03 


2.96 


4.02 


2.97 


4.01 


2.99 


h 


6 


4.85 


3,53 


4.84 


3.55 


4.82 


3.57 


4.81 


3.59 


6 


7 


5.66 


4.11 


5.65 


4.14 


5.63 


4.16 


5.61 


4,19 


7 


8 


6.47 


4.70 


6.45 


4.73 


6.43 


4.76 


! 6.41 


1,73 


8 


9 


7.28 


5.29 


7.26 


5.32 


7.23 


5.35 


1 7.21 


5,38 


9 


10 


8.09 


5.88 


8.06 


6.91 


8.04 


5.95 


1 8.01 


5.98 


10 
11 


11 


8.90 


6.47| 


8.87 


6.50 


8.84 


6.54 


8.81 


6.58 


12 


9.71 


7.05 


9.68 


7.10 


9.65 


7.141 9.61 


7,18 


12 


la 


10.52 


7.64 


M).48 


7.69 


10.45 


7.73J 10.42 


7.78 


13 


14 


11.33 


8.23| 


11.29 


8.28 


11,25 


8.33 11.22 


8.38 


14 


15 12.14 


8.821 


12.10 


8.87 


12.06 


8.92 


12.02 


8.97 


15 


16j 12.94 


9.40| 


12.90 


9.46 


12.86 


9.52 


12.82 


9.57 


16 


1713.75 


9.99 


13.71 


10.05 


13.67 


10.11 


13.62 


10.17 


17 


18 14.56 10.58 


14.52 


10.64 


14.47 


10.71 


14.42 


10.77 


18 


19 15.37111.17 


15.32 


11.23 


15,27 


11.30 


15.22 


11.37 


19 


20 
21 


16.18 


11.76 
12.34 


16.13 

16.94 


11.83 


16.08 

16.88 


11.90 


16.03 


11.97 20| 


16.99 


12.42 


12.49 


16.83 


12.56 


21 


22 


17.8012.93 


17.74 


13.01 


17.68 


13.09. 17.63 


13.16 


22 


■23 


18.61|13.52 


18.55 


13.60 


18.49 


13.68j 18.43 


13.76 


28 


24 


19.4214.11 


19.35 


14.19 


19,29 


14.28 


19.23 


14.36 


24 


25 20.23; 14.69 


20.16 


14.78 


20.10 


14.87 


20.03 


14.96 


25 


26;21.03 15.28 20.97 


15.37 


20.90 


15.47 


20.83 


16.56 


26 


27121.8415,87 


21.77 


15.97 


21.70 


16.06 21.63 


16.15 27 


28 22.65,16.46 


22.58 


16.56 


22.51 


16.65: 22.44 


16.75' 28 


29 23.46 17.05 


23.39 


17.15 


23.31 


17.25 


23.24 


17.35, 29 


39 24.27 17,63 


24.19 


17.74 


24.12 


17.84 


24.04 


17.95J SO 


31 25.08 18.22 


25.00 


18.33 


24.92 


18.44 


24.84 


18.55 31 


3225.89 18.81 


25.81 


18.92 


25.72 


19.03 


25,64 


19.15 32 


33 26.70 19.40 ;26.61 


19.51 


26.53 


19.63 


26.44 


19.74 33 


34 27.51 1 19.98 127.42 


20.10 


27.33 


20.22 


27.24 


20.34! S4 


35 28.32,20,57 28.23 


20.70 


28.13 


20.82 


28.04 


20.94 


35 


86129.12 21.16 


29.03 


21.29 


28.94 


21.41 


28.85 


21.54 


S6 


37:29.93!21.75 


29.84 


21.88 


29.74 


22.01 


29.65 


22.14 


S7 


38 30.74 


22,34 


30.64 


22.47 


30.55 


22.60 


30.45 


22.74 


SB 


39'31.55 


22,92 


31.45 


23.06 


31.35 


23.20 


31.25 


23.33 


3«) 


40 


32.36 


23,51 


32.26 


23.65 


32.15 


23.79 


33.05 


23.93 


40 


41 


33.17 


24.10 


33.06 


24.24 


32.96 


24.39 


32.85 


24.53 


41 


4233.98 


24.69 


33.87 


24.83 


33.76 


24.98 


33.65 


25.13 


42 


43;34.79 


25.27 


34.68 


25.43 


34.57 


25.58 


34.45 


25.73 


43 


44,35.60 


25.86 


35.48 


26.02 


35.37 


26.17 


35.26 


26.33 


44 


45 36.41 


26.45 


136.29 


26.61 


36.17 


26.77 


36.06 


26.92 


45 


4637.21 


27.94 


37.10 


27.20 


36.98 


27.36 36.86 


27.52 46l 


47138.02 


27,63 


37.90 


27.79 


37.78 


27.96 37.66 


28.12 


47 


48 38.83 


28,21 


38.71 


28.38 


38.69 


28.55 38.46 


28.72 


48 


49!39,64 


28^0 


39.62 


28.97 


39.39 


29.15 39.26 


29.32 


49 


50 


40.45 
Dep. 


29.39 
Lat, 


40.32 


29.57 
Lat. 


40.19 
Dep. 


29.74 
Lat. 


40.06 
Dep. 


29,92 
Lat, 


50 

'4,3 

cn 


Dep. 


64 Deg. 


53|Deg. 


oSiDeg. 


53] Deg. 



TRAVERSE TABLE- 



^-,36 Deg.i 36xDeg. .36iDeg.j 36f Deg.j ^ 



Lat.jDep. Lat.lDep. Lat. Dep. Lat. Dep 



5141. 

52 42, 

53 42. 

54 43. 

55 44. 

56 45. 
5746. 

58 46. 

59 47. 
60,48. 



2629.98' 

07130.56 

88131.15 

6931.74: 

50 32.33;; 

30 32.92;: 

I1I33.5O 

92134.09 

73134.68 

54:35.27 



61 49.35'35.85 

62 50.1636.44 

63 50.97 37.03 
6451.78 37.62 

65 52.69 38.21 

66 53.4038.79 

67 542039.38 

68 55.0139.97 

69 55.82;40.56 
70,56.63141.14 



1.07' 49.1 
1.66|,49.J 
■.25i50.i 
'.84| 51.. 
1,44 52.1 
1.03 53.( 
1.62 53.: 
1.21: 64.1 
1.80 55.. 
.39 66.: 



30.341 
30.93 
31.53 
32.12 
32.72 
33.31 
33.90 
34,50i 
35.09 
35.69 



40.86 30.. 
41.67 31. 
42.47 31. 



,43.27 
144.07 
,44.87 
45.67 
:46.47 
'47.27 
:48.08 



32.: 



8165.5347.61 

82 66.S4'48.20 

83 67.1548.79 

84 67.96i49.37 

85 68.77 49.96 

86 69.58 50.55 

87 70.38 51.14 

88 71.19 51.73 

89 72.00 52.31 

90 72.8152.90 

9173.62,53.49 

92 74.43;54.08 

93 75,24 54.66 

94 76.05 55.25 

95 76.8655.84 

96 77.67156.43 

97 78.4757.02 
98:79.28 57.60 
99 80.09,68.19 

100:80.90 58.78 



57.26 41.98 
58.06;42.57i 
58.87I43.I7 
59.68l43.76 
60.4S|44,35 
61.29:44.94 
62.10145.53 
62.90 48.12 
63.7146.71 
64.52|47,30 

65.32147,90 

66.13!48,49 
66.93|49.08 
67.74149.67 
68.55 50.26 
69.35 50.85 
70.1651.44 
70,97 52,04 
71.77 52.63 
72.5863.22 

73.39 53,81 
74.1954.40 
75,00 54,99 
75,8155,58 
76,6156,17 
77.42 56.77 
78,23 57,36 
79,03 57.95 
79,84 58.54 
80.64 59.13 



57.07 

57.88 
58.68 



42,23 
42,83 
43.42 



56.89 
57.69 
58.49 
59.49 44.02 59.29 
60.09 



60.29 
61.09 
61.90 
62.70 
63.50 
64.31 

65,11 

65.92 
66.72 
67.52 
68.33 
69.13 
69.94 



44.61 

45.21 60.90|45. 

46.80 61,70 46. 

46.40 

46.99 

47.59 



.30[ 59 
.90| 60 

:.5oi 61 
.10, 62 
.69 1 63 
1.291 64 
1.891 65 
.49 66 
1.09 67 
1.691 68 
69 



62.50 
63. .30 
64.10 



48,18 
48.78 
49.37 
49,97 
50,56 
51,15 
51.75 
70. 74152.34 
71,54152.94 
72,35 53u63 j 

54.13 i 

54.72 
55,32 
55.91 
56-51 
57.10 
57.70 
58.29 
79.58 68,89 
80.39 59.48 



75 

47! 76 
07i 77 
67 78 
27 79 
87 80 



64.90 

65.70 

66.50 

67.31 

68,11 

68.91[61, 

69,71j52, 

70.51152, 

71,3l|53. 

72.11163. 



Dep,| Lat. |Dep.| Lat. Dep, Lat. 1 Dep.' Lat 



83 

26' 84 

86' 85 

46' 86 

05: 87 

65 88 

25 89 

85 90 

1.46 91 
i,06 92 
..64 93 
1.24 94 
1.84 95 
.44 96 
1.04 97 
1.64 98 
.23 99 
,83 100 



54 Peg. l53^Deg. 53xDeg.ii53JDeg,Ct 



TRAVERSE TABLE, 




32.74 
33.54 
34.34 
35.14 
35.94 
36.74 
37.54 
38.33 
39.13 
39.93 



24.6 

25.28 

25.88 

26.48 

27.08 

27.68 

28.29 

28.89 

29.49 

30.09 



Dep. Lat. 
53 Deg. 



32.64124.82 
33.43|25.42 
34.23:26.03 
35.02i26.63 
35.82'27.24 
36.6227.84 



37.41 

38.21 
39.00 
39.80 



28.45 
29.05 
29.66 
30.26 



Dep. Lat 



523Deg. 



32.5324.96 
33.32 25.57 
34.1126.18 
34.9126.79 
35.70 27.39 
36.49 28.00 
37.29,28.61 
38.08l29.22 
38.87129.83 
39.6730.44 

Dep.' Lat. 
52iDeg. 



32.4225.10 
33.21125.71 
34.0026.33 
26.94 
27.55 
28.16 
28.77 
29.39 
30.00 
30.61 



Dep. Lat.Lj 

I m 

52iDeg.p 



TRAVERSE TABLE. 



US 



37^Deg. 37iDeg. 37|Deg 




! 40.73 
141.53 
[42.33 
143.13 

,43.92 
56 44.72 
5745.52 
5846.32 

59 47.12 

60 47.92 



61 

63 
64 
65 
66 
67 
68 
69 
70 

71 
72 
73 
74 
75 
76 
77 
78 
79 
80 

81 

82 
83 
84 
85 
86 
87 
88 
89 
90 

91 
92 
93 
94 
95 
96 
97 
98 
99 
100 



30. S9 
31.29 
31.90 
32.50 
33.10 
33.70 
34,30 
34.91 
35.51 
36.11 



36.71 
37.31 
37.91 

38.52 
39.12 
39.72 
40.32 
40.92 
41.53 
42.13 



42.73 
43.33 
43.93 
44.531 
45.14 
45.74 
46.34 
46.94 
47.54 
48.15 



48.75 
49.35 
49.95 
50.55 
51.15 
51.76 
52.36 
52.96 
53.56 
54.16 



54.77 
55.37 
55.97 
56.57 
57.17 
57.77 
58.38 
58.98 
59.58 
60.18 



Dep. Lat. 
53 Peg. 



Lat. 



40.60 
41.39 
42.19 
42.98 
43.78 
44.58 
45.37 
46.17 
46.96 



Dep. 



4'*.76 36.32 



48.56 
49.35 
50.16 
50.94 
51.74 
52.54 
53.33 
54.13 
54.92 
55.72 



56.52 
57.31 
58.11 
58.90 
59.70 
60.50 
61.29 
62.08 
62.88 
63.68 



42.98 
43.58 
44.19 
44.79 
46.40 
46.00 
46.61 

47.21 

47.82 
48.42 



64.48 
65.27 
66.07 
66.86 
67.66 
68.46 
69.25 
70.05 
70.84 
71.64 



72.44 
73.23 
74.03 
74.82 
75.62 
76.42 
77.21 
78.01 
78.80 
79.60 



30.87 
31.48 
32.08 
32.69 
33.29 
33.90 
34.50 
35.11 
35.71 



36.92 
37.53 
38.13 

38.74| 
39.34 
39.95' 
40.55' 
4L16i 
41.77i 
42.37 



Lat.Dep. 

40.46B1.05 
41.2531.66 
42.05l32.26 
42.84132.87 
43.63 33.48 
44.43l34.09 
45.22|34.70 
46.0135.31 
46.81 35.92 
47.60 36.53 



49.03 
49.63 
50.24 
50.84 
51.46 
52.06 
52.66 
53.27 
53.87 
64.48 



56.33 43.22 
57.i2l4S.83 



55.08 
55.69 
56.29 
56.80 
57.50, 
68.11! 
58.71' 
59.32 
».92 
60.53 



Dep. Lat, 

52|Deg. 



64.2649.31 
65.0549.92 
65.85 50.53 
66.b4l5i.l4 
67.4Si5L74 
68.23 52.35 
69.0252.96 
69.82|53.57 
70.61154.18 
71.40 54.79 



Lat, 



56.14 
56.93 

57.72 
58.51 
59.30 
60.09 
60.88 
61.67 
62.46 
63.26 



64.05 
64.84 
65.63 
66.42 
67.21 
68.00 
68.79 
69.58 
70.37 
71.16 




Dep 



43.47 
44.08 
44.69 
45.30 
45.92 
46.53 
47.14 
47.75 
48.37 
48.98 



49.59 
60.20 
50.81 
51.43 
52.04 
52.65 
53.26 
53.88 
54.49 
66.10 



51 

52 
53 
64 
65 
56 
67 
58 
59 
60 

61 

62 
63 
64 
65 
66 
67 
68 
69 
70 

71 

72 
73 
74 
75 
76 
77 
78 
79 
80 

81 
82 
83 
84 
85 
86 
87 
88 
89 
90 



52iDeg 



lU 



TRAVERSE TABLE. 



o 

1 


38 Deg. 


38iDeg.| 


38^Deg. 


38iDeg. 


5 

en 
1 


Lat. 

0.79 


Dep. 

0.62 


Lat. 
0.79 


Dep, 

0.62 


Lat. 

0.78 


Dep. 

0.62 


Lat. 

0.78 


Dep. 


0.63 


2 


1.58 


1.23 


1.57 


1.24 


1.67 


1.24 


1.56 


1.25 


2 


3 


2.36 


1.85 


2.36 


1.86 


2.35 


1.87 


2.34 


1.88 


3 


4 


3.15 


2.46 


3.14 


2.48 


3.13 


2.49 


3.12 


2.50 


4 


5 


3.94 


.'?,08 


3.93 


3.10 


3.91 


3.11 


3.90 


3.13 


5 


6 


4.73 


3.69 


4.71 


3.71 


4.70 


3.74 


4.68 


3.76 


6 


7 


6.52 


'4.31 


5.50 


4.33 


6.48 


4.36 


5.46 


4.38 


7 


8 


6.30 


4.93 


6.28 


4.95 


6.26 


4.98 


6.24 


5,01 


8 


9 


7.09 


5.54 


7.07 


6.67 


7.04 


6.60 


7.02 


6.63 


9 


10 
11 


7.88 
8.67 


6.16 
6.77 


7.85 
8.64 


6.19 
6.81 


7.83 
8.61 


6.23 
6.86 


7.80 
8.68 


6.26 


10 
11 


6.89 


12 


9.46 


7.39 


9.42 


7.43 


9.39 


7.47 


9.36 


7.61 


12 


13 


10.24 


8.00 


10.21 


8.06 


10.17 


8.09 


10.14 


8.14 


13 


14 


11.03 


8.62 


10.99 


8.67 


10.96 


8.72 


10.92 


8.76 


14 


15 


11,82 


9.23 


11.78 


9.29 


11.74 


9.34 


11.70 


9.39 


15 


16 


12.61 


9.85 


12.57 


9.91 


12,52 


9.96 


12.48 


10.01 


16 


17 


13.40 


10.47 


13,36 


10,62 


13,30 


10.58 


13.26 


10.64 


17 


18 


14.18 


11.08 


14.14 


11.14 


14.09 


11.21 


14.04 


11.27 


18 


19 


14.97 


11.70 


14,92 


11,76 


14.87 


11.83 


14,82 


11.89 


19 


20 


16.76 


12.31 


15.71 


12.38 


16.65 


12.45 


16,60 


12.52 


20 


21 


16.65 


12.93 


16.49 


13.00 


16.43 


13.07 


16.38 


13.14 


21 


22 


17.34 


13.54 


17.28 


13.62 


17.22 


13.70 


17.16 


13.77 


22 


23 


18.12 


14.16 


18.06 


14.24 


18.00 


14.32 


17.94 


14.40 


23 


24 


18.91 


14.78 


18.85 


14.86 


18,78 


14.94 


18.72 


15.02 


24 


25 


19.70 


16.S9 


19.63 


15.48 


19.67 


15.56 


19.50 


15.65 


25 


26 


20.49 


16.01 


20.42 


16.10 


20.3* 


16.19 


20.28 


16.27 


26 


27 


21.28 


16.6S 


21.20 


16.72 


21.13 


16.81 


21.06 


16.90 


27 


28 
29 


22.06 
22.85 


17.24 


21.99 


17.33 


51.91 


17.43 


21.84 
22.62 


17.53 
18.15 


28 


17.85 


22.77 


17.96 


22.70 


J 8.06 


29 


30 
31 


23.64 

24.4S 


18.47 


23.56 


18.57 
19.19 


23.48 
2426 


18.68 
19.30 


23.40 

24.18 


18.78 
19.40 


30 


19.09 


24.34 


31 


32 


25.22 


19.70 


^.13 


19.81 


26.04 


19.92 


24.96 


20.03 


32 


33 


26.00 


20.32 


26.92 


20.43 


26.83 


20.64 


25.74 


20.66 


33 


34 


26.79 


20.93 


26.70 


21.05 


26.61 


2U17 


26.62 


21.28 


34 


35 


27.68 


21.65 


'27.49 


21.67 


27.39 


21.79 


27.30 


21.91 


36 


36|28.37 


22.16 


,28.27 


22.29 


28.17 


22.41 


28.08 


22.53 


36 


87 


29.16 


22.78 


129.06 


22.91 


28.96 


23.03 


28.86 


23.16 


37 


38 


29.94 


23.40 


129,84 


23.63 


29.74 


23.66 


29.64 


23.79 


38 


39 


30.73 


24.01 


ISO.63 


24.14 


30.62 


24.28 


30.42 


24.41 


39 


40 


31.52 


24.63 31.41 


24.76 


31.30 


24.90 


31.20 


25.04 


40 


41 


32.3] 


26.24 132.20 


26.38 


32.CS 


26.62 


31.98 


25.66 


41 


42 


33.10 


25.86 


32.98 


26.00 


32.87 


26.15 


32.76 


26.29 


42 


43 


33.88 


26.47 


33.77 


26.62 


33.65 


26.77 


33.63 


26.91 


43 


44 


34.67 


27.09 


34.65 


27.24 


i34.43 


27.39 


34,31 


27.54 


44 


46 


35.46 


27.70 


36.34 


27.86 


36.22 


28.01 


36,09 


28.17 


45 


46 


36.25 


28.32 


36.12 


28.48 


36.00 


28.64 


35.87 


28.79 


46 


47 


37.04 


28.94 


36.91 


S9.10 


36,78 


29,26 


36.65 


29.42 


47 


48137.82 


29.55 


37.70 


29.72 


37,67 


29,88 


37.43 


30.04 


48 


49138.61 


30.17 


38.48 


30.34 


38.36 


30,50 


38.21 


30.67 


49 


50J39.40 


30.78 
Lat. 


39.27 


30.95 


39,13 
Dep, 


31,13 


38.99 


31.30 
Lat, 


50 


In 


Dep. 


Dep, 


Lat. 


Lat. 


Dep, 




s 




52 Deg. 


'51|Deg. 


51^ 


Deg. 


&U 


Deg. 


s 



TRAVERSE TABLE. 




16 



TRAVERSE TABLE. 



CD 
1 


,39 Deg. 


39iDeg. 


391 Deg. 


39|Deg. 




Lat 
0.78 


Dep. 
0.63 


Lat 


iDep. 


Lat. 
0.77 


Dep. 


Lat. 
0.77 


Dep. 

0.64 


0.77 0.63 


0.64 


2 


1.56 


1.26 


1.55 1.27 


1.54 


1.27 


1.54 


1.28 


2 


a 


2.33 


1.89 


2.32 1.90 


2.3] 


1.91 


2.31 


1.92 


3 


4 


3.11 


2.52 


3.10 2.53 


3.09 


2.64 


3.08 


2.56 


4 


5 


3.8£ 


3.15 


3.87 


3.16 


3.86 


3.18 


3.84 


3.20 


5 


6 


4.66 


3.78 


4.65 


3.80 


4.65 


3.82 


4.61 


3.84 


6 


7 


5.44 


4.41 


5.42 


4.43 


5.40 


4.45 


6.38 


4.48 


7 


8 


6.22 


5.03 


6.20 


5.06 


6.17 


6.09 


6.15 


6.12 


S 


9 


6.99 


5.66 


6.97 


6.69 


6.94 


.').72 


6.92 


.5.75 


9 


iO 


7.77 


6.29 


7.74 


6.33 


7.72 


6.36 


7.69 


6.39 


10 
11 


11 


8.55 


6.92 


8.52 


6.96 


8.49 


7.00 


8.46 


7.03 


12 


9.33 


7.55 


9.29 


7.59 


9.26 


7.63 


9.23 


7.67 


12 


13 10.10 


8.18 


10.07 


8.23 


10.03 


8.27 


9.99 


8.31 


13 


14 10.88 


8.81 


10.84 


8.86 


10.80 


8.91 


10.76 


8.95 


14 


15 11.66 


9.44 


11.62 


9.49 


11.67 


9.54 


11.53 


9.59 


15 


16 12.43 


10.07 


12.39 


10.12 


12.35 


10.18 


12.30 


10.23 


16 


17 13.21 


10.70 


13.16 


10.76 


13.12 


10.81 


13.07 


10.87 


17 


18 13.99 


11.33 


13.94 


11.39 


13.89 


11.45 


13.84 


11.61 


18 


19 14.77 


11.96 


14.71 


12.02 


14.66 


12.09 


14.61 


12.15 


19 


20 


15.54 


12.59 
13.22 


15.49 
16.26 


12.65 


15.43 


12.72 
13.36 


15.38 
16.15 


12.79 
13.43 


20 
21 


21 


16.32 


13.29 


16.20 


22 


17.10 


13.84 


17.04 


13.92 


16.98 


13.99 


16.91 


14.07 


22 


23 


17.87 


14.47 


17.81 


1455 


17.76 


14.63 


17.68 


14.71 


23 


24 18.65 


15.10 


18.59 


15.18 


18.52 


15.27 


18.45 


15.35 


24 


25| 19.43 


15.73 


19.36 


16.82 


19.29 


15.90 


19.22 


16.99 


25 


26|20.21 


16.36 


20.13 


16.45 


20.06 16.54 


19.99 


16.63 


26 


27|20.98il6.99 


20.91 


17.08; 


20.83 


17.17 


20.76 


17.26 


27 


28 21.7617.62 


21.68 


17.72: 


21.61 


17.81 


21.53 


17.90 


28 


29 22.5418.25 


22.46 


18.35! 


22.38 


18.46 


22.30 


18.54 


29 


30 


23.31118.88 


23.23 


18.98 
19.61 


23.15 


19.08 
19.72| 


23.07 

23.83 


19.18 301 


31 


24.091 19.51 


24.01 


23.92 


19.82 


31 


32'24.87|20.14 


24.78 


20.25 


24.69 


20.35 


24.60 20.46 


32 


33 25.65 20.77 


25.65 


20.88 


25.46 


20.991 


26.37 


21.10 


33 


34 26.42l21.40 


26.33 


21.51 


26.24 


21.63 


26.14 


21.74 


34 


35 27.20 22.03 


27.10 


22.14 


27.01 


22.26 


26.91 


22.38 


85 


36'27,98 22.66 


27.88 


22.78 


27.78 


22.90l 


27.68 


23.02 


36. 


3728.7523.28 


23.65 


23.41 


28.65 


23.63 


28.45 


23.66 


37 


38 29.5323.91 


29.43 


24.04 


29.32 


24.17 


29.22 24.30 


38 


39 30.31,24.54 


30.20 


24.68 


30.09 


24.81 


29.98 24.94 


39 


40 
41 


31.09 


25.17 


30.98 25.311 


30.86 


25.44 
26.08 


30.75 


25.58 
26.22 


40 
41 


31.86 


25.80 


31.75 


25.94 


31.64 


31.52 


42 


32.64 


26.43 


32.52 


26.57 


32.41 


26.72 


32.29 


26.86 


42 


43 


33.42 


27.06 


33.30 


27.21 


33.18 


27.35 


33.06 


27.60 


43 


44 


34.19 


27.69 


34.07 


27.84 


33.96 


27.99 


33.83 


23.14 


44 


45 


34.97 


28.32 


34.85 


28.47 


34.72 


28.62 


34,60 


28.77 


45 


46 


35.76 


28.95 


35.62 


29.10 


35.49 


29.26 


35.37 


29.41 


46 


47 


36.53 


29.68 


36.40 


29.74 


36.27 


29.90 


36.14 


30.05 


47 


4ft 


37.30 


30.21 


37.17 


30.37 


37.04 


30.53 


36.90 


30.69 48 


49 


38.08 


30.84 


37.95 


31.00 


37.81 


31.17 


37.67 


31.33 49 


50 
♦J 

Q 


38.86 


31.47 
Lat. 


38.72 
Dep. 


31.641 

1 

Lat. 


38.58 


J1.80 


38.44 
Dep. 


31.97 5D 


Dep. 


Dep. 


Lat. 


Lat.j 




51 Deg. 1 


50fDeg.l 


50iDeg.|l 


501 Deg. If 


il 



TRAVERSE TABLE. 




IS 



TRAVERSE TABLE. 



• 


40 Deg. 


40iDeg. 


40iDeg. 


40|Deg.| 


P. 

I 


Lat. 


Dep. 


Lat. Dep, 


Lat. 

0.76 


Dep. 
0.65 


Lat, 

0,76 


Dep. 

0.65 


1 


0.77 


0.64 


0.76! 0,65 


2 


1.53 


1.29 


1,53 1.29 


1.52 


1.30 


1.62 


1.31 


2 


3 


2.30 


1.93 


2,29 1,94 


2.28 


1.95 


2.27 


L96 


3 


4 


3.06 


2,67 


3.05 


2.68 


3.04 


2.60 


3.03 


2.61 


4 


6 


3.83 


8.21 


3.82 


3.23 


3.80 


3.25 


3.79 


3.26 


5 


6 


4.60 


3.86' 


4,68 


3.88 


4.66 


3.90 


4.55 


3.92 


6 


7 


S.36 


4.50! 


5,34 


4.52 


6:32 


4,55 


6.30 


4.67 


7 


8 


6,13 


5,14| 


6,11 


5.17 


6.08 


5,20 


6.06 


6.22 


8 


9 


6.89 


5,79 


6.87 


6.82 


6.84 


5.84 


6.82 


5.87 


9 


10 


7.66 


6.43; 

- ,| 


7,63 6.46 

1 

8,40 7,1L 


7.60 
8.36 


6.49 
7.14 


7.58 

1 

8.33 


6.53 
7.18 


10 
11 


11 


8.43 


7.07 


12 


9.19 


7.71 


9.16 


7.75 


9.12 


7,79 


1 9.09 


7.83 


12 


13 


9.96 


fi.36 


9,92 


8.40 


9.89 


8,44 


9.85 


8.49 


13 


14 10.72! 9.00 110.69 


9.06 i 10.66 


9.09i 10,61 


9.141 141 


16 11.49' 9.64 11.45i 9.69 11.41 


9.74: 11,36 


9.79 


15 


16 12.2C!l0.28 :12.2i:i0.34 12.17 


10,39: 12.12 


10.44 


16 


17 13.02 10.93 113.9710.98 J12.93 


11,04 12,88 


11.10 


17 


18'l3.79, 11.57 il3..74'll. 63 Il3.69 


11,69 13,64 


11.75 


18 


19 14.53 12.21 ;14.60 12.28 


14.45 


li;.34 14,39 


12.40 


19 


20 15.32112.86116.26:12.92 
21116.09113.60 il6.03 13.57 


15.21 
15.97 


12.99 15.15 
13.64 15.91 


13.06 


20 
21 


13.71 


22116.8614.14 16.7914.21 


16.73 


14.29' 16.67 


14.36 


22 


23117.62 14.78^17.5514.86 


17.49 


14.94' 17.42 


15.01 


23 


24il8.39 15.43 18.32 16.51 


18.25 


15.59| 18.18 


15.67 


24 


25I19.15 16.07 19.08 16.15 


19.01 


16.241 18.94 


16.32 


25 


2619.92 16.71 i 19.84 16.80 


19.77 


16.89 


19.70 


16.97 


26 


27,20.68117.36 120.6117.45 


20.53 


17.54 


20.45 


17.62 


27 


28l21.45il8.C0 21.37 18.09 


21.29 


18.18 


21.21 


18,28 


28 


29i22.22il8.64 22.1318.74 


22,06 


18.83 


21.97 


18.93 


29 


30 
31 


22.98jl9.28i22.90,19.38 
23.75 19.93 '23.66'20.03 


22,81 


19.48 


:22.73 
23.48 


19.58 
20.24 


30 

31 


23.67 


20.13 


32 


24.61 20.67 '24.42 20.68 


24.33 


20.78 


24.24 


20.89 


32 


33 


25.28 21,21 23.19 21.32 


25.09 


21.43 


25.00 


21.54 


33 


34 


26.05 21.85 25,95 21.97 


25.85 


22.08 


25.76 


22.19 


34 


35 


26.81 22.50 26.71 22.61:26.61 


22.73 


26.51 


22.85 


35 


36 


27.58 23.14:27.48 23.26:27.37 


23.38 


27.27 


23.50 


36 


37 


28.34 23.78 128.24 23. 91j 28.13 


24.03 


28.03 


24.15 


37 


38 


29.11:24.43 ;29.00 24.55: 28.90 


24.68 


28.79 


24.80 


38 


39 


29.88 25.07 |29.77 25.20 29.66 


25.33 


29.54 


25,46 


39 


40 


30.64j25.7r'S0.53 25.84 


30.42 


25.98 


:30.30 


26.11 


40 
41 


4131.4126.36 


31.29 26.49 


31.18 


26.63 


■31,06 


26. 7S 


42 32.17;27.00 


32,06 27,14j 31.94 


27.28 


31,82 


27.42 


42 


43 32.9427.64 


32.82 27.781 32.70 


27.93 


32.58 


28.07 


43 


44 33.7128.28 


33.68 28.43 33.46 


28.58 


33,33 


28.72 


44 


46 34.47:28.93 


34,36 29.08 34,22 


29.23: 34.09 


29.37 


46 


46,33.24,29.57 


35.11 29.72 |34,98 


29.87 34.85 


30.03 


46 


47j36.00i30.21 


35.87 30.37| 35.74 


30.52^35.61 


30.68 


47 


48 36.77lS0.85 


36.6431.03j!S6,60 


31,17 36.36 


31.33 


48 


49 


37.5431.50 


37.4031.66 


37.26 


31,82 i37,]2 


31.99 


49 


50 


38.30 32.14 


38.16 32,31 


38.02 


32.47 


37.88 


32.64 


50 


Dep, Lat. 


Dep. Lat. 


Dep. 


Lat, 


Dep. 


Lat. 




60 Deg. 


49|Deg. 


49^ Deg. 


49lDeg. 



TRAVERSE TABLE. 




120 



TRAVERSE TABLE. 



5 

1 


41 Deg. 


41iDeg. 


41iDeg. 


41|Deg. 



55 


Lat. 
0.75 


Dep. 
0.66 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.75 


0,66 


0.75 


0.66 


0.76 


0,67 


1 


9. 


1.51 


1.31 


1..50 


1,32 


1.60 


1.33 


1.49 


1.33 


2 


3 


?,.2fi 


1.97 


2.26 


1.98 


2.25 


1.99 


2.24 


2.00 


3 


4 


3.02 


2.62 


3.01 


2.64 


3.00 


2.65 


2.98 


2.66 


4 


5 


3.77 


3.9,8 


3.76 


3.30 


3.74 


3.31 


3.73 


3.33 


5 


6 


4.53 


3.94 


4.51 


3.96 


4.49 


3.98 


448 


4.00 


ti 


7 


5.28 


4.59 


6.26 


4.62 


5,24 


4.64 


6.22 


4.66 


'; 


8 


B.04 


6.25 


6.01 


5.27 


5.99 


5.30 


5.97 


6.33 


8 


< 9 


6.79 


5.90 


6.77 


5.93 


6.74 


5.96 


6.71 


6.99 


9 


10 


7.55 


6.56 


7.52 


6.59 


7.49 


6.63 


7.46 


6.66 


10 


11 


8.30 


7.22 


8.27 


7.25 


8.24 


7.29 


8.21 


7.32 


11 


S 12 


9.06 


7.87 


9.02 


7.91 


8.99 


7.96 


8.95 


7.99 


12 


; 13 


9.81 


8..53 


9.77 


8.57 


i 9.74 


8.61 


9.70 


8,66 


13 


. 14 


10.57 


9.18 


10.53 


9.23 


I1O.49 


9.28 


10.44 


9.32 


14 


i 15 


11.32 


9.84 


11.28 


9.89 


111.23 


9.94 


H.19 


9.99 


16 


: Ifi 


12.08 


10.50 


12.03 


10.55 


!ll.98 


10.60 


11.94 


10.65 


16 


,17 


12.83 


11.15 


12.78 


11.21 


I12.73 


11.26 


12.68 


11.32 


17 


i 18 


18.58 


11.81 


13.53 


11.87 


i 13.48 


11.93 


13.43 


11.99 


18 


; 19 


14.34 


12.47 


14.28 


12.53 


14,23 


12.59 


14.18 


12.65 


19 


20 
. 21 


15.09 
15.85 


13.12 
13.78 


15.04 


13.19 


14.98 


13.25 


14.92 


13.32 


20 
21 


15.79 


13.85 


15.73 


13.91 


15.67 


13.98 


' 22 


16.60 


14.43 


16.54 


14.51 


16,48 


1468 


16.4114.65 


22 


; 23, 


17.36 


15.09 


17.29 


15.16 


17.23 


15.24 


17.16ll5.S2 


23 


24 


18.11 


15.75 


I8.04| 15.62 


17.97 


15.90 


17.9115.98 


24 


25 


ia87 


16.40 


18.80116.48 


18.72 


16.57 


18.65ll6.66 


2i. 


26 


19.62 


17.06 


119.551 17. 14 


'19.47 


17,23 


19.40 


17.31 


2b 


, 27 


20.38 


17.71 


,20.30117.80 


20.22 


17.89 


20.14 


17.98 


27 


28 


21.13 


18.37 


21.05il8.46 


20.97 


18,65 


20,89 


18.64 


S8 


23 


21.89 


19.03 


,21.80119.12 


21.72 


19.22 


21.64 


19.31 


29 


30 
31 


22.64 


19.68 


22.56|19.78 


|22.47 


19.88 


22.38 

1 


19.98 


30 
31 


23.40 


20.34 


23.3120.44 


!23.22 


20.54 23. is|20.64 


^2 


24.15 


20.99 


!24.06 21.10 23.97 


21.20 23.87|21.3] 


!*> 


33 


24.91 


21.65 


24.81-21.76 |24.72 


21.87 i24.62l21.97 


33 


34 


25.66 


22.31 


25.56122.42 |25.46 


22.63 i25.37i22,64 


34 


35 


26.41 


22.96 


26.31 23.08 |26.2l!23.19 26.1l!2S.3] 


35 


3tt 


?7.17 


23.62 


27.07 '23. 74 126.96 


23.85 :26.86 


23.97 


36 


37 


27.92 


24.27 


27.82 24.40| 127. 71 


24.52 ?7.60 


24.64 


37 


3« 


28.68 


24.93 


28.67 25.061 28.46 


25.18 28.35 


25.30 


38 


39 


29.43 


25.59 


29.32i25.71 29.21 


25.84129.10 


25.97 


39 


• 40 
ll 


30.19 

30.94 


26.24 
26.90 


30.0726.37 
30.83l27.03 


29.86 


26.50 


29.84 


26.64 


40 


30.71 


27.17 


30.59 


27.30 


41 


42 


31.70 


27.55 


31..58 27.69 


31.46 27.83 


31.33 


27,97 


42 


43 


32.45 


28.21 


32.33 28.35 32.21 28.49 f32.08i28.63 


43 


44 


33.21 


28.87 


33.08 29.01 


32.95 


29.16 32.83 29.30 


44 


45 


33.96 


29.62 '33.83 29.67 


133.70 


29.82 133.67 i29.97 


45 


46 


34.72 


30.18 34.58 30.33 


34.45 


30.48 


34.32|30.63 


46 


47 


35.47 


30.83 35.34 30.99 


35.20 


31.14 


35.06 31.30 


47 


48 


36.23 


31.49 


36.09 31.65 


35.96 


31.81 


35.81 31.96 


48 


49 


36.98 


32.15 


36.8432.31 


36.70 


32.47 


36.56 32.63 


49 


bO 


37.74 
Dep. 


32.80 
Lat. 


37.6932.97 

1 

Dep. Lat. 


37.46 


33.13 


37.3033.29 
Dep.' Lat. 


60 

CO 

S: 


Dep. 


Lat. 


o 


49 Deg. 


481 D«g. 


48^Deg.|i48jDeg.| 



TRAVERSE TABLE. 



121 



41 De". 



;41|Deg. 41^Deg. 41|Deg. ,-, 

7~ ' 55' 

Lat. Dep.; r" 




^ Dep. I Lat. Dep. Lat.' Dep. Lat. jDep. I Lat. 



£ J49 DesrHH^Pp.: 4S;, Dpg. '48^l3eg. 



23 



123 



TRAVERSE TABLE, 



E5' 


42 Deg. 


42fDeg. 


j42^Deg. 


423 Ueg. 





Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.74 


0.67 


0.74 


0.67 


0.74 


0.68 


0.73 


0.68 


1 


2 


1.49 


1.34 


1.48 


1.34 


1.47 


1.35 


1.47 


1.36 


2 


3 


2.23 


2.01 


2.22 


2.02 


2.21 


2.03 


2.20 


2,04 


3 


4 


2.97 


2.68 


2.96 


2.69 


2.95 


2.70 


2.94 


2.72 


4 


5 


3.72 


3.35 


3.70 


3.36 


3.69 


3.38 


3.67 


3,39 


5 


6' 4.46 


4.01 


4.44 


403 


4.42 


4.05 


4.4) 


4.07 


6 


7 5.20 


4.68 


5.18 


4.71 


5.16 


4.73 


5.14 


4.75 


7 


s' 5.95 


5.35 


5.92 


5,38 


5.90 


5,40 


6.87i 5.43 


8 


9 6.69 


6.02 


6.66 


6.05 


6.64 


6,08 


6.61 


6.11 


9 


10 


7.43 


6.69 


7.40 


6.72 


7.37 


6.76 


7.34 
8.08 


6.79 

7.47 


10 
11 


11 


8.17 


7.36 


8.14 


7.40 


6.11 


7.43 


12 


8.92 


8.03 


8.88 


8.07 


8.85 


8.11 


8.81 


8.15 


12 


13 


9.66 


8.70 


9.62 


8.74 


9.58 


8.78 


9.55 


8.82 


13 
14 


14 10.40 


9.37 


10.36 


9.41 


10.32 


9.46 


10.28 


9.50 


1511.16 


10.04 


11,10 


10.09 


11.06 


10.13 


ill.Ol 


10,18 


15 


1611.89 


10,71 


11,84 


10.76 


11.80 


10.81 


111. 75] 10.86 


16 


17112.63 


11,38 


12.58 


11.43 


12.53 


11.48 


il2.48lll.54 


17 


18113.38 


12.04 


13.32 


12.10 


13.27 


12.16 


113.2212.22 


18 


19 14.12 


12.71 


14.06 


12.77 


14.01 


12.84 


13.9512.90 


19 


20:14.86 


13.38 


14.80 


13.45 


14.75 


13.61 


14.69 13.68 


20 


21I15.6I 


14,05 


15.54 


14.12 


15.48 


14.19 


15.42' 14.25 


21 


2216.35 


14.72 


16.28 


14.79 


16.22 


14.86 


16.1614.93 


22 


23117,09 


15.39 


17.02 


15.46 


16.96 


15.54 


16.89' 15.61 


23 


24 17.8416.06 


17.77 


16.14 


17.69 16.21 


17.6216.29 


24 


2518.5816.73 


18.51 


16.81 


18.43 16.89 


j 18.36 16.97 


25 


26:19.3217.40 


19.25 


17.48 


19.17 17.57 


19.09 17.65 


26 


27i20.06 18.07 


19.99!i8.15: 


19.91 18.24 


19.8318.33 


27 


28.20.8lll8.74 


20.73' 18.83i 


20.64 


18.92 


20.56 19.01 


28 


29 21,5519.40 


21.47 


19.50 


21.38 


19.59 


21.30 19.69 


29 


30 22,29 20.07 

31 23.04'20.74 


22,21 
22.95 


20.17 


22.12 
22.86 


20.27 
20.94 


22.03 20.36 

22.76 21.04 


30 
31 


20.84 


32:23.78|21.41 


23.6921.52 


23.5921.62 


23.50,21,72 


32 


33;24.52,22.08 


24.43I22.I9 


24.33'22.29 


24.23 22.40 


33 


34 25.2722.75 


25.17 22.86 


25.07 22.97 


24.97 23.08 


34 


35 26.0123.42 


.25.9123.53 


25.8023.65 


125,70 23.76 


35 


36 26.75 24.09 


26.65 24.21' 


26.54 24.32 


i26.44 24.44 


36 


37 27.50 24.76 


27.39 24.88 


27.28 25.00 


i27.17 25.12 


37 


38 28.24 25.43 


28.13 25.55 


28.02 23.67 


127.90 25. 79 38 


39 28.98 26.10 


28.8726.22 


28.75 26.35 


128.6426.47 39 


40;29. 73 26.77 

1 1 


29.6126.89 


29.49 27.02 


'29.37 27. 15 40 


4130.4727.43 


30.3527.57 


30.23 27.70 


30.1127.83: 41 


4231.2128.10 


'31.0928.24 


30.97 28.37 


,'30.84 28.51; 42 


43 31.96 28.77 


31.8328.91 


31.7029.05 


31.58 29.19' 43 


4432.7029.44 


32.57 29.58 


32.4429.73 '32.31 29.87' 44J 


45'33.44 30.11 


33.31 30.26 


33.18 30.40 


133.04 30.55 45 


46 34.1830.78 


34.05 30.93 


33.91 31.08 


33.7831.22 46 


47 34.93 31.45 


34.7931.60 


34.65 31.75 


34.51 31.90. 47 


48:35.67 32.12 


35.53 32.27 


35.39 32.43 


35.25 32.58 48 


49 36.41 32.79 


36.27 32.93 


36.1333.10 


35.9833.26 


49 


50 37.16 33.46 


37.01,33.62 


36.8633,78 


36.7233.94 


50 


■4^ 


Dep.l Lat. 


Dep. Lat. 


Dep,' Lat. 


Dep. Lat. 




48 Deg. 


473 Deg. 


47^Deg. 


:47fDeg. 


Q 



TRAVERSE TABLE. 




124 



TRAVERSE TABLE. 



o 


43 Deg. 


43iDeg. 


43^Deg. 433Deg. 


d 


s 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 1 Lat. 


Dep. 


¥ 


1 


0.73 


0.68 


0.73 


0.69 


0.73 


0.69 0.72 


0.69 1 


2 


1.46 


1.36 


1.46 


1.37 


1 1.45 


1.38 1.44 


1.38 2 


3 


2.19 


2.05 


2.19 


2.06 


! 2.18 


2.07 2.17 


2.07 3 


4 


2.93 


2.73 


2.91 


2.74 2.90 


2.75' 2.89 


2.77 4 


5 


3.66 


3.41 


3.64 


3.43, 3.63 


3.44 3.61 


3.46 6 


6 


4.39 


4.09 


4.37 


4.11' 4.35 


4.13! 4.33 


4,15| 6 


7 


6.12 


4.77 


6.10 


4.801; 5.08 


4.82 5.06 


4,84; 7 


8 


5.85 


5.46 


5.83 


5.481 5.80 


6.51 5.78 


6.53 8 


9 


6.58 


6.14 


6.56 


6.171 6.53 


6.20 i 6.60 


6.22 9 


10 


7.31 


6.82 


7,28 


6.851: 7.25 


6.88' 7.22 

1 


6.92 10 


11 


8.04 


7.50 


8.01 


7.54 7.98 


' 1 
7.57 7.95! 7.61 111 


12 


8.78 


8.18 


8.74 


8.22' 8.70 8.26 8.67 8.30 12 


13 9.51 


8.87 


9.47 


8.91! 9.43 8.95 9.39 8.99 13 


14 10.24 


9.55 


10.20 


9.59i 10.16 9.64 lO.llI 9,68 14 


15 10.97 


10.23 


10.93 


10.281 10.88 10.33 10.84 10,37 15 


16 


11.7010.91; 11.65 


10.961 11.61 11.01 n.56tll.06 16 


17 


12.43,11.59! 12.38 


11.65 12.33 11.70 12.28 11.76 17 


18 


13.1612.28 13.11 


12.33 13.06 12.39 13.00 12.45 18 


19 


13.90112.961,13.84 13.02 13.78 13.08 13.7213.14 19 


20 


14.63 13.641 14.57 13.70 14.51 13.77 14.4513.83 20 


21 


15.36 14.321 15.30 14.39! 15.23 14.46 15.17 14.52 21 


2216.09 15.00 16.02116.07 16.% 15.14 15.8915.21 22 


23 16.82 15.69; 16.75 15.76 ItJ.eS 15.83 16.6115.90 23 


24! 17.55 16.37 17.48 16.44 17.41 16.52 17.3416.60 24 


25 18.28 17.05,18.2117,13 18.13 17.21 18.06 17.29 25 


26 19.02 17.73 18.94 17.81 18.86 17.90 18.78 17.98 26 


27 19.76 18.41 19.67 18.50 19.-^9 18.59 19,dO-i« g? 27" 


28 20.48 19. IQ 20.39 19.19 20.31 19.27 20.23 19.36 281 


29 21.21.19.78; 21.12 19.87 21.04 19 96 20.95 20,05 291 


30 


21,94j20,46| 21,85 20.56, 21,76 20.65 21.67 20.75 30 


31 


22.67'21.14! 22.58 21.24 22.49 21.34 22.39 21.44 31 


32 


23.4021.82 23.31 21.93 23.jil 22.03 23.12 22.13 32 


33 


24,13 Z2-.51. 24.04 22.61 23.94 22.72 23.84 22.82 33 


34j24.87 23.19 24.76 23.30 24.66 23.40 24.56 23.51 34 


35125.60 23.87 25.49 23.98 25,39 24.09 25.28 24.20 35 


36 26.33 24.55 26.22 24.67 26. li 24.78 26.01 24.89 36 


3727.06 


25.23, 26.95 25.35 26.84 25.47; 26.73 25.59 37 


3827.79 


25.92 27.68 26.04 27.56 26.16' 27.45 26.28 38 


39 28.52 


26.60 28.4126.72 28.29,26.85 28.1726.97 39 


40 


29.25 


27.28 29.13 27.41 29.01|27.53; 28.89 27.66 40 


41 


29.99 


27.96 29.86 28.09 29.74 28.22 29.6228.36 "il 


42i30.72 


28.64! 30.5928.78 30.47 28.91 30.34 29.04 42 


4331.45 


29.33 31.32 29.46 31.19 29.60 31.06 29.74 43 


44132.18 


30.01 32.05 30.15 31.92 30.29 31.7830,43 44 


45 32.9130.69 32,7830.83 32.6430.98 32.5131.12 45 


4633.6431.37 33.5131.52 33.37 31.66 33.23 31.81 46 


47 34.37 82.05 34.2332.20 34.09 32.35 33.95 32.50 47 


48 35.10 


32.74 34.96 32.89 34.82 33,04 34.67 33.19 48| 


49 


35.84 


33.42 35.69 33.57 35.5433.73 35.40 33.88 491 


60 


36.57 


34.10 ;36.42 34.26 36.27 


34.421 36.12 34.58 50 


CO 

St! 


Dep. 


Lat. Dep. Lat. 


Dep. 


Lat. Dep. Lat. ^^ 


47 Deg.''463Deg. 


46i 


Deg. 46^ 


Deg. 


B 



TRAVERSE TABLE. 




126 



TRAVERSE TABLE. 




TRAVERSE TABLE. 




128 



NATURAL SINES. 



IV, A Table of Natural Sines, calculated to five places of 
figures, for every J)Iinute. 

Natural Sines are Decimals bearing the same proportion 
to Unity or 1 that the Sine of the corresponding number of 
Degrees and Minutes bears to Radius or Sine of 90°. That is, 
1 is assumed as the Nat. Sine of 90°, and the Table calculated 
accordingly. 

Explanation of the Table. 

To find the JValural Sine of any number of Degrees and Minutes. 

U the degrees be less than 45, look for them at the Top of 
the Columns, and for the Minutes at the left-hand ; but if more 
than 45, look for them at the Bottom, and for the Minutes at the 
right-hand ; under or over the Degrees and against the Minutes 
will be the Natural Sine required. 

The reverse of this will give the Degrees and Minutes cor- 
responding to any Natural Sine. 

To calcfidate the JVorthing or Southing, ^c. for any Course and 
Distance, by JYat. Sines. 

Find the Nat. Sine and Co-Sine of the Course, and into each 
of these multiply the Distance ; the Products will be the Lati- 
tude and Departure required. 

Example. 

Required the Latitude and Departure for 6 Chains aiid 22 
Links, on a Course JV. 38° 27' W. 

Nat. Sine of 380 27', 0.62183 Nat. Co-Sine 0.78315 
6.22 6.22 



124366 
124366 
373098 

3.8677826 
jin^wer. Northing 4.87 



156630 
156630 
469890 

4.8711930 
Westing 3.87 



A TABLE OF NATURAL SINES. 




130 



A TABLE OF NATURAL SINES. 



M 


5Deg. 


f 6 Deg. 


jTD 


eg- 


8 Deg. 


9 Deg. 


M 

60 


N. S.iN.CS 


^I\. S. N.CS.iN. S.jN.CS 


N. S. N.CS 


N. S.|N.CS 


C 


08716 99619 10453 99452!l2187 


99255813917 99027 


15643 


98769 


1 


74S 


17 482 


49 216 


51 


946i 23 


672 


64 


59 


2 


774 


- 14 511 


46 245 


49 


975 


19 


701 


60 


58 


3 


803 


12 540 
09 569 


43 274 


44 


14004 


15 


730 


55 


67 


4 


831 


40 


302 


40 


033 


11 


758 


51 


56 


5 


860 


07 597 


37 


331 


37 


061 


06 


787 


46 


55 


6 


889 


04 626 


34 


360 


33 


090 


02 


816 


41 


64 


7 


918 


02: 655 


31 


389 


30 


11998998 


845 


37 


53 


8 


947 99599,' 684 


28 


418 


26 


148 


94 


873 


32 


58 


9 


976 


96 713 


24 


447 


22 


177 


to 


902 


28 


61 


10 


09005 


94) 742 


21 


476 


19 


205 


86 


931 


23 


50 


11 


034 


9I| 771 


18 


504 


15 


234 


82 


959 


18 


49 


12 


063 


88 


800 


15 


533 


11 


263 


73 


988 


14 


48 


13 


092 


86 


829 


12 


562 


08 


292 


73 


16017 


09 


47 


14 


121 


83 


858 


69 


591 


04 


320 


69 


046 


04 


46 


15 


150! 80 


887 


06 


620 


00 


349 


65 


074 


00 


45 
44 


1609179;99o78 


10916;99402 


12649 


99197 


1437898961 


16103 


98696 


17 


208 


75 


945 99399 


678 


93 


407 


57 


132 


90 


43 


18 


237 


72 


973 


96 


706 


89 


436 


53 


160 


86 


42 


19 


266 


70 


11002 


93 


736 


86 


464 


48 


189 


81 


41 


20 


295 


67 


031 


90 


764 


82 


493 


44 


218 


76 


40 


21 


324 


64 


060 


86 


793 


78 


622 


40 


246 


71 


39 


22 


353 


62 


089 


83 


822 


75 


551 


36 


275 


67 


38 


23 


382 


59 


118 


8(H 851 


71 


580 


31 


304 


62 


37 


24 


411 


56 


147 


77 880 


67 


608 


27 


333 


57 


36 


25 


440 


53 


176 


74 906 


03 


637 


23 


361 


52 


36 


26 


469 


51 


206 


70 


937 


60 


666 


•19 


390 


48 


34 


27 


498 


48 


234 


67 


966 


56 


695 


14 


419 


43 


33 


28 


527 


45 


263 


64 


995 


52 


723 


10 


447 


38 


32 


29 


556 


42 


291 


60 


13024 


48 


752 


06 


476 


33 


31 


30 


585 


40 


320 


57 


063 


44 


781 


02 


505 


29 


30 

29 


31 


09614 99537U 1349 


99354 


13081 


99141 


14310 


98897 


16533 


98624 


32 


642 


34 378 


51 110 


37 


838 


93 


66i 


19 


2S 
27 


33 


671 


31 407 


47 


139 


33 


887 


89 


591 


14 


34 


700 


28 436 


44 


168 


29 


896 


81 


.620 


09 


26 


35 


729 


26 


465 


41 


197 


26 


926 


80 


64S 


04 


25 


36 


758 


23 


494 


37 


226 


22 


954 


76 


677 


00 


24 


37 


787 


20 


523 


34 


254 


18 


9S2 


71 


700 


98595 


23 


38 


818 


17 


552 


31 


283 


14 


15011 


67 


734 


90 


22 


39 


845 


14 


580 


27 


312 


10 


040 


63 


763 


85 


21 


40 


S74 


11 


609 


24 


341 06 


069 


58 


792 


80 


20 


41 


903 


08 


638 


20 


370 02 


097 


54 


820 


75 


19 


42 


932 


06 


667 


17 


39999098 


126 


49 


849 


70 


18 


43 


961 


03 


696 


14 


427 


94 


155 


45 


878 


66 


17 


44 


990 


00 


725 


10 


456 


91 


184 


41 


906 


61 


16 


45 


10019 


99497 


754 


07 


485 


87 


212 


36 


935 


56 


15 


46 


10048 


99494 


1178399303 


1351499083: 


15241 


9883^ 

27 


16964 


98551 


14 


47 


077 


91 


812 00 


543 


79 


270 


992 


46 


13 


48 


106 


88 


840'99297 


572 


75 


292 


23 


17021 


41 


12 


49 


135 


85 


889 


93 


600 


71 


327 


18 


050 


36 


11 


50 


164 


82 


898 


90 


629 67 


356 


14 


078 


31 


10 


51 


192 


79 


927 


86 


658 63 386 


09 


107 


26 


9 


52 


221 


76 


956 


83 


687 59 414 


05 


136 


21 


8 


53 


250 


73 


985 


79 


716 55; 442 


00 


164 


16 


7 


54 


279 


70 


12014 


76 


744f 511 471 


98796 


193 


11 


6 


55 


308 


67 


043 


72 


7731 47] 500 


91 


222 


06 


5 


56 


337 


64 


071 


69 


802i 4S| 529 


87 


250 


01 


4 


57 


366 


61 


100 


65 


831 1 39 557 


82 


279 


98496 


3 


58 


395 


58 


129 


62 


8601 35! 686 


78 308 


91 


2 


59 
M 


424 

N.CS 


55 


158 


58 


8891 3l| 615 


73 336 


86 

N. S. 


I 
M 


N. s.! 


N.CS. 


N. S. 


N.CS.N. Sj 


n.cs.In. s.sn.cs.I 


84 Deg.j 


83 Deg.i 


82 Deg4' 


81 1 


)eg.i 


BO E 


)eg. 



A TABLE OF NATURAL SlNES. 



131 



M 



10 Deg.,n Deg.j 


12 Deg. 13 Deg. 


14 Deg. 




iV. s. 
17365 


N.CS'iN. S. N.CS 


N. S.,N.CS N. S. N.CS 


N. S. N.CS 


M 

60 


98481 19081 


98163 


2079197815 22495'97437 


24192 97030 


1 


393 


76i 109 


57 


820 809 


623 


430 


220! 023 


59 


2 


432 


71 138 


52 


848 803 


552 


424 


249 015 


58 


3 


451 


66' 167 


46 


877 797 


580 


417 


277 008 


57 


4 


479 


6I3 195 


40 


905 791 


608 


411 


305 001 


66 


5 


508 


551 224 


35 


9331 784 


637 


404 


333 96994 


65 


6 


537 


60, 252 


29 


962 778 


665 


398 


362 987 


54 


7 


565 


45 281 


24 


990 772 


693 


391 


390 980 


63 


8 


594 


40 309 


18 


21019 766 


722 


384 


418 973 


52 


9 


623 


35 338 


12 


047! 760 


750 


378 


446' 966 


51 


10 


651 


30 366 


07 


076i 754 


778 


371 


474S 969 


50 


11 


680 


25 395 


01 


104 748 


807 


366 


503; 952 


49 


12 


708 


201 423 98096 


132' 742 


835 


358 


531 946 


48 


13 


737 


14 452 90 


1611 735 


863 


351 


5591 937 


47 


14 


766 


093 481 84 


189' 729 


892 


345 


587 930 


46 


15 


794 


04| 509 79 


218 723 920 


338 


615 923 


45 


16 


17823 


98399,19538'98073 


21246 97717*22948 
275 71 If 977 


97331 


24644 96916 


~44 


17 


852 


94 566 


67 


325 


672 


909 


43 


18 


880 


89 595 


61 


303 


705^23005 


318 


700 


902 


42 


19 


909 


83 


633 


56 


331 


698 033 


311 


728 


894 


41 


20 


937 


78 


652 


50 


360 


692 062 


304 


756 


887 


40 


21 


966 


73 


6S0 


44 


388 


686 090 


298 


784 


880 


39 


22 


995 


68 


709 


39 


417 


680 118 


291 


813 


873 


38 


23 


18023 


62 


737 


33 


445 


673 146 


284 


841 


866 


37 


24 


052 


57 


766 


27 


474 


667 175 


278 


869! 858 


36 


25 


081 


52 


794 


21 


602 


661 203 


271 


897 


851 


35 


26 


109 


47 


823 


16 


530 


655 231 


264 


925 


844 


34 


27 


138 


41 


851 


10 


559 


648 260 


257 


953 


837 


33 


28 


166 


36 


880 04 


587 


642 288 


251 


982 


829 


32 


29 


195 


31 


90897998 


616 


636 316 


244 


25010 


822 


31 


.30 
31 


224 


25 


937| 92 


644 
21672 


630; 345 
97623 23373 


237 


038 


815 


30 
29 


1.8252 


98320'19965 97987 


97230 


25066 96807 


32 


281 


15 994; 81 


701 


617 401 


223 


094 


800 


28 


33 


4509 


10200221 75 


729 


611 429 

604J 458 


217 


122 


793 


27 


34 


338 


04 


051! 69 


758 


210 


151 


786 


26 


35 


367 


98299 


079 


63 


786 


593 


486 


203 


179 


778 


25 


36 


395 


94 


108 


58 


814 


692 


514 


196 


207 


771 


24 


37 


424 


88 


136 


52 


843 


585 


542 


189 


235 


764 


23 


38 


452 


83 


165 


46 


871 


579 


571 


182 


263 


756 


22 


39 


481 


77 


193 


40 


899 


573 


599 


176 


291 


749 


21 


40 


509 


72 


222 


34 


928 


666 


627 


169 


320 


742 


20 


41 


538 


67 


250 


28 


956 


560 


656 


162 


348 


734 


19 


42 


567 


61 


279 


22 


985 


553 


684 


165 


376 


727 


18 


43 


595 


56 


307 


16 


22013 


547 


712 


148 


404 


719 


17 


44 


624 


50 


336| 10 


041 


541 


740 


141 


432 


712 


16 


45 

1:6 


652 


45 


364! 05 


070 


534 


769 
^3797 


134 


460 


705 


15 

14 


1868198240 


20393 97899 


22098 97528 


97127 


25488 96697 


47 


710 


34 421 93 


126 521 


825 


120 


516 


690 


13 


48 


738 


29 450 87 


155 


615 


853 


113 


545 


682 


12 


49 


767 


23 478 81 


183 


508 


882 


106 


673 


676 


11 


SO 


795 


18 507! 75 


212 


602 


910 


10(y 


601 


667 


10 


51 


824 


12 535 69 


240 


496 


938 


093 


629 


660 


9 


52 


852 


07 563! 63 


2681 489 


966 


086 


657 


653 


8 


53 


881 


01 592! 57 


2971 4835 995 


079 


685 


645 


7 


54 910 98196 6201 51 


325 


476'24023 


072 


713 


638 


6 


55 938; m 649| 45- 353 


470 051 


065 


741 


630i 5 


56 9671 85 


677 39; 382 


463 079 


058 


769 


623! 4 


57 9951 79 


706 33^ 410 


457 108 


051 


798 


6I5I 3 


58 190241 74 


7341 27; 438 


450 136 


044 


826 


6081 2 


59 052| 68 


7631 21 467 


444 164 


037 


854 


600 1 


m 


N.CSIN. S. 


N.CS'isi. S.N.CS'N. S.JN.CS'N. S. 


N.CS 


N. S. 


M^ 


79 Deg. 


78 Deg.i77 Deg.'76 Deg.»75 Deg. 


_l 



133 



A TABLE OF NATURAL SINES. 



15 Deg.|16 Deg.| 


17 Deg.jlS Deg.| 


19 Deg. 




Mn. S. 


N.CS In. s.in.cs 


N. S. 


N.CS N. S. 


N.CS 


N. S.IN.CS 

j 


M 


25882 


96593 27564 96126 


29237 


9563030902 


95106 


32557 94562 


60 


1 


910 


585 


592 


118 


265 


622 


929 


097 


584 


542 


59 


2 


938 


678 


620 


110 


293 


613 


957 


088 


«12 


633 


58 


3 


966 


570 


648 


102 


321 


605 


985 


079 


639 


523 


57 
56 
55 


4 


994 


562 


676 


094 


348 


596 


31012 


070 


667 


514 


5 


26022 


555 


704 


086 


376 


588 


040 


061 


694 


504 


6 


050 


547 


731 


078 


404 


579 


068 


062 


722 


495 


64 

53 


7 


079 


540 


759 


070 


432 


571 


096 


043 


749 


485 


8 


107 532l 


787 


062 


460 


562 


123 


033 


777 


476 


52 


9 


135 


624 


815 


064 


487 


554 


151 


024 


804 


466 


51 


10 


163 


517 


843 


046 


515 


545 


178 


015 


832 


457 


50 


11 


191 


509 


871 


037 


543 


536 


206 


006 


859 


447 


49 


12 


219 


602 


899 


029 


571 


528 


233 


94997 


887 


438 


48 


13 


247 


494 


.927 


021 


599 


519 


261 


988 


914 


428 


47 


14 


275 


486 


955 


013 


626 


511 


289 


979 


942 


418 


46 
45 
44 


16 


303 


479 


983 


006 


654 


502 


316 


970 


969 


409 


16 2633i 


96471 


28011 


95997 


29682 


95493 


31344 


94961 


32997 


94399 


17 


359 


463 


039 


989 


710 


485 


372 


952 


33024 


390 


43 


18 


387 


456 


067 


981 


737 


476 


399 


943 


051 


380 


42 


19 


415 


448 


095 


872 


765 


467 


427 


933 


079 


370 


41 


20 


443 


440 


123 


964 


793 


459 


454 


924 


106 


361 


40 


21 


471 


483 


160 


956 


821 


450 


482 


915 


134 


351 


39 


22 


500 


425 


178 


948 


849 


441 


510 


906 


161 


342 


38 


23 


528 


417 


206 


940 


876 


433 


537 


897 


189 


332 


37 


24 


556 


410 


234 


931 


904 


424 


565 


888 


216 


322 


36 


26 


584 


402 


262 


923 932 


415 


593 


878 


244 


313 


35 


26 


612 


394 


290 


915 960 


407 


620 


869 


271 


303 


34 


27 


640 


386 


318 


907 987 


398 


648 


860 


298 


293 


S3 


28 


668 


379 


346 


898 30015 


389 


675 


851 


326 


284 


32 


29 


696 


371 


374 


890 043 


380 


703 


842 


353 


274 


SI 


30 


724 


363 


402 


882 071 


372 


730 


832 


381 


264 


30 
29 


31 


26752 


96356 


28429 


95874 30098 


95363S31758 


94823 


33408 


94254 


32 


780 


347 


467 


865 


126 


354 


786 


814 


436 


245 


28 


S3 


808 


340 


485 


857 


154 


345 


813 


805 


463 


235 


27 


34 


836 


332 


513 


849 


182 


337 


841 


795 


490 


225 


26 


-35 


864 


324 


641 


84] 


209 


328 


868 


786 


518 


215 


25 


36 


892 


316 


669 


832 


237 


319 


896 


777 


546 


206 


24 


87 


920 


308 


597 


824 


265 


310 


923 


768 


573 


196 


23 


38 


948 


301 


625 


816 


282 


301 


951 


758 


600 


186 


22 


39 


976 


293 


662 


807 


320 


293 


979 


749 


627 


176 


21 


4027004 


286 


680 


799 


348 


284^32006 


740 


655 


167 


20 


41 


032 


277 


708 


791 


376 


275 


034 


730 


«82 


157 


19 


42 


060 


269 


736 


782 


403 


266 


061 


721 


710 


147 


18 


43 


088 


261 


764 


774 


431 


267 


089 


712 


737 


137 


17 


44 


116 


253 


792 


766 


459 


248 


116 


702 


764 


127 


16 


46 
46 


144 


246 
96236 


820 


757 


486 


240 


144 


693 


792 


118 

94108 


15 
14 


27172 


28847|95749 


30514 


95231 


32171 


94684 


33819 


47 


200 


230 


876 


740 


542 


222 


199 


674 


846 


098 


13 


48 


228 


222 


903 


732 


570 


213 


227 


666 


874 


088 


12 


49 


256 


214 


931 


724 


697 


204 


254 


656 


901 


078 


11 


60 


284 


206 


959 


715 


626 


195 


282 


646 


929 


068 


10 


51 


312 


198 


967 


707 


653 


186 


309 


637 


956 


058 


9 


52 


340 


190 


29015 


698 


680 


177 


337 


627 


983 


049 


« 


53 


368 


182 


042 


690 


708 


168 


364 


618 


34011 


039 


7 


54 


396 


174 


070 


681 


736 


159 


392 


609 


038 


029 


6 


56 


424 


166 


098 


673 


763 


160 


419 


599 


065 


019 


6 


66 


452 


158 


126 


664 


791 


142 


447 


590 


093 


009 


4 


57 


480 


150 


154 


656 


819 


133 


474 


580 


120 


93999 


3 


58 


508 


142! 182 


647 


846 


124 


502 


571 


147 


989 


o 


-59 


636 


134 


209 


639 


874 


115 


629 


561 


175 


979 


1 


M 


N.CS 


N. S. 


N.CS 


nTsT 


N.CS 


N. S. 


N.CS 


N. S. 


N.CS 


N. S. 


1m 


74 Deg. 


73 Deg. 


72 ] 


Deg. 


171 Deg. 


70 Deg. 



A TABLE OP NATURAL SINES. 



m 



20 Deg. 21 Deg. 



9 
10 
11 
12 
13 
14 
J5 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

~3i 
32 
33 
34 
35 
36 
37 
38 
39 
40 



N.CS N. S. N.C8 

34202 93969 35S37 93358 
229 959 864 348 
257 949 891 33 " 
284 939 918 327 
311 929 945 31o 
339 919 973 3O0 
366 909 360U0 21».> 
393 899 027 285 
421 889 054 274 
26 
25i 



22 DegT23 Deg.,24 Deg. 



443 879 081 

475 869 108 

503 859 135 243 

530 849 162 232 

557 839 190 222 

584 829 217 211 

012 819 244 ! 201 
34639 93809 36271 93190 

666 

694 

721 

748 

775 

803 

830 

857 

884 

912 

939 

966 

993 
35021 



35048 
075 
102 
130 
157 
183 
211 
239 
266 
293 
411 320 
42 347 
431 375 
441 402 
45! 429 
4635456 
47 484 
48] 511 

49 538 

50 565 
511 592 



799 298 180 

739 325 169 

779 352 159 

769 379 148 

759 406 137 

748 434 12 

738 461 



.V. S. N.CtJ IN". S. N.CS { N. S. N.CS 
37461 92718 390739205040674 91355 

488 707 100; 039t 700 343 

515 687 127 028; 727 331 

542 686 153| 0161 753 319 

5691 675 180 005; 780 307 

C.S5' 664 20791994- 806 293 

022: 653 234' 982; 833 283 

649' 642 260 971 860 272 

676; 6-31 237 959 836 260 

703: 620 314 948 913 248 

730' 609 341 936c 939 236 

757; 698 367 925 966 224 

784| 587 394i 914; 992 212 

811i 576 421 90241019 200 

838: 565 443, 891 045! 188 

865 554 474 879 072 176 
37892 92543,39501 91888 41098 91164 

919i 532 528 856 125 152 

946i 52L 655 845, 151 140 

9731 510; 581 8335 178 128 



728 488 



lib 
106 



999 j 499 608; 8225 204 116 

38026) 488^ 6351 810'; 231 104 

0o3' 477 661 ! 799 o57 092 






619 
647 
674 
701 
728 
755 
782 
59! 810 

."mJn.csIn. s. 



718 515 095 

708 542 084 

698 569 074 

688 596 063 

677 623- 052 

667 650 042 

93657 36677 93031 

647 704 O20 

637 731 010 

626 758 92999 

616 785 988 

606 812 978 

596 839; 967 

585 867 956 

575 894! 945 

565 S21 935 

555 948 924 

544 975: 91'3 

534 37002 902 

524 029. 892 

514 056 881 

93503 37083 92870 

493, 110 859 

483^ 137 849 

472 164 838 

4S2, 191 827 

452| 218 816 

441 j 245 805 

4311 272 794 



38295 92377 39902-91694;41496 90984 
322' 366 928' 683] 522 972 
3491 355 9551 671| 549 960 
376| 343 982 660 575 945 
403 332.40008 648J 602 936 



O8O; 466: 688 
1071 455' 715 
1341 444 741 



787^ 284 080 
775.; 310 068 
764< 337 056 



161, 432 768! 752i 363 044 

188 421 795 74U 390 032 

215' 410 822! 729J 416- 020 

241' 399 848i 718? 443 008 

268 388 875! 7061 469 90996 



M 
60 
59 
58 
57 
56 
55 
64 
53 
52 
51 
50 
49 
48 
47 
46 
_45 
44 
43 
42 
41 
40 
39 
33 
37 
36 
35 
34 
S3 
32 
31 
30 



430 321I 035 

456 310) 062 

483 2995 088 

510 28"! 115 

537 276' 141 

564 2651 198 

591 264i 195 

617 243i 221 

644 231| 248 

671 220 . 27J> 

33898 92209-40301 

725 193"; 328 

752 186i 355 

778 175' 381 

164 1 403 

152! 434 

141i 461 



420 
410' 
400 
389 
379 
368 



636j 628i 924 

625 655 911 

613: 681 i 899 

601] 707i 887 

590j 734: 875 

6781 760 863 

666] 7871 651 

655: 613 639 

543j 840 826 

_53i; 666; 814 
9151914189290802 



805 
832 
859 



886 130i 483 

293 784 9121 119; 514 

326 773 939 107j 541 

353 762' 9661 0961 567 

380 751 993 085; 594 

407 74039020 073i 621 

434 729 046 082 647 



508 919 
496} 946 
484' 972 
472i 993 
461.42024 



449, 
437 
425 
4i4 
402 
390 
378 
366 



N.CS N. S. N.CS'N. S.'iN.CSlN. S.I N.CS 



051 
077 
104 
130 
156 
183 
209 
235 



790 
778 
766 
753 
741 
729 
717 
704 
692 
680 
668 
655 
643 
NTs? 



29 

28 
27. 
2Q 
25* 

2< 
23' 
22' 
21^ 
20 
19 
18 
17 
16 

if 
14 
13 
12 
11 
10: 



M 



69 Deg.i68 Deg.67 Deg,;66 DegJ65 Deg.i 
36 



131 



A TABLE OF NATURAL SINES. 




25 Deg j26 Deg 27 Deg,|28 Deg. 29 Deg, 

5r~ilN7^!^?7^NXis N. S. N.CSiN. S.N.CS n'/'sTnTcs 



45399 8910M6947 88295 
425 087i 973 281 
451 074 999 
477 061 47024 
503 048 050 
529 035 
554 021 
580 0081 
606 8899 
632' 881] 



16 42683 90433,44255 89674s458I3 B8888M7358 88075 



709 4215 281 

736 408| 307 

762: 396? 333 

788 3831 359' 

815i 3711 385' 

841 3583 411 

8&7 346i 437 




383 062 

409 048 

434, 034 

460: 020 



662) 839 875 

649J 865 8621 

6361 891, 848| 

6231 917' 835; 

610 942 822| 466 006|49014 

597 968 808| 

584- 994 7958 

24 894 3341- 464 571-46020 782| 662 965 

25 920 32 li 490 558i 046 768S 588 951 

KAid f\ia tckS at a qq-v 



511 87993 
537 97« 



26 946 309 516 545 072 7553 614 937 

27^ 972 296 542| 532? 097: 74l| 639 923 

28 999 284 568' 5195 123 72^ 665 909 

29 43025 271 594 606; 149 715! 690 896 

30 051 259 1 620 493/ 175 701 ? 716 

3143077 90246|44646 89480^46201 8868sk7741 87868 

32 104 233S 672! 467| 226; 674] 767 854 

33 130 221, 698,' 454) 252; 661:- 793 840 



34 156 

35 182 

36 209 

37 235 

38 261 



287 
313 
340 
366 
392 
418 
445 



2083 7241 

196| 7501 

183s 776j 

1711 802! 

168 

148| 

133 

120 

108' 

095 



441 278 647> 818 

428 304 634! 844 

Am 330 620,? 869 

402' 355 607i 895 



39 

40 
41 

42 
43 
44 

45 

464347190057,45036 
47 497 045] 06; 

6231 032 

549' 019 

675 007 

602 89994 

628| 981 

654| 968! 

680j 956 

706 943 



733 
759 
785 
811 




826 
812 
798 
784 
770 
756 
743 
729 
715 
701 
687 
673 



48481 
506 
532 
557 
583 
608 
634 
659 
684 
710 
735 
761 
1301 786 
811 
837 
862 

48888 
913 
938 
964 
989 



xM.CS M 



87462! 60 
448; 59 
434; 58 
4201 57 
406: £6 
3911 55 
377 64' 
363 
349 
335 
321 
306 
292 
278 
264 
250 



87235 
221 
207 
193 
178 
164 
150 
136 
121 
107 
093 
079 
064 
050 
036 



040 
065 
090 
116 
141 
166 
192 
217 
242 
49268 
293 
318 
344 
369 
394 
419 
445 
470 
495 
521 
546 
671 
596 
622 

87659 49647,86805 
645= 672! 791 
631; 697! 777 
617] 723 
603' 748 
589^ 773 
575j 798 
56! 824 
546! 849; 
632: 874' 
518 899 

924i 

950 

975 



504 
490 
476 



87021 
007 

86993 
978 
964 
949 
935 
921 
906 
892 
878 
863 
849 
834 
820 



762 
748 
733 
719 
704 
690 
675 
661 
646 
632 1 
617 



53 
52 
51 
50 
49 
48 
47 
46 
45 
44 
43, 
42 
41 
40 
39 
38 
37 
36 
35 
34; 
33 
32 
31 
30 

"29 
28 
27 
26 
26 
24 
23 
22 
21 
20 
19 
18 
17 
16 

14 

13 
12 
11 
10 
9 
8 
7 

I 
4 
3 
2 
1! 



N. ;l^. n.cs n. s.rrn 



64 Peg. 83 Deg. 62 Peg. 61 Peg. 60 Peg. 



A TABLE OF NATURAL SINES, 



135 



30 Deji. 31 Deg. 32 Deg, 



M N. s. N.rs r- 



25 



50000 
025 
050 
076 
101 
126 
151 



86603 
588 
573 
559 
544 
530 
515 



176 501 

2011 486 
227,1 471 
252! 457 
277 442 
302 427 
327 413 
352 398 
377 384 
86369 
354 
340 



16 50403 



428 
453 
478 
503 
528 
553 
678 
603 
628 
654 
679 
704 
729 
754 

50776 
804 
829 
854 
879 
904 
929 
954 
979 

51004 
029 
054 
079 
104 
129 

51164 
179 
204 
229 
264 
279 
304 
329 
364 
379 
404 
429 
454 
479 



8614S 62275 85-i49 63754 84324 



N.CS 



325 
310 

296 
281 
266 
251 
237 
2"i2 
207 
192 
178 
163 



51604 
529 
55^ 
5'h 
60-4 
628 
65[ 
67' 
70l 
Kb 
758 
77 f- 
80i 
828 
862 
87 

6190ii 
927 
652 
977 

52002 
026 
051 
076 
101 
126 
151 
175 
200 
225 
250 



X.r 8 ?v S.lN^Ci 

8'5717 52992 84806 

70253017 789 

687 041 1 774 

672 066 759 

091 743 

115 728 

140: 712 

164' 697 




85476 5338(i 84567 

461 J 411 542 

446f 436 626 

431| 460! 511 

416J 484| 495 

401! 5091 480 

385j 6341 464 

370i 558 i 448 

3S5i 583: 433 

340' 607! 417 

325! 632 402 

310f 656 386 

294} 681 1 370 

279' 705 355 

264 730i Sii 



iJ3 299 234 779| 308 

119 324 218j 8041 292 

104 349 203| 8281 277 

089- 374 188| 8631 26 J 

074 399 1731 877 245 

059 423 157; 902| 230 

045 448 142'; 926; 214 

030 473 127' 961 198 

015 498 ll?i 975 182 

000 522 096^54lX)0' 167 

85985 547 081 j 024 161 

970» 57« 066! 049 135 „„^, ..^ ««- wu 

956 657 05l| 073 120 533 163 976 181 

941 621 035 ; 097 104 ; 567 14 7 57000 165 

85926 52646 85020 54122 84088;6558i 83131 57024 82148 

911 671 005. 146 072i 605 115 047 132 

896 696 84989; 171 057? 630! 098 071 115 

881 720 974r 195 041- 654 082 096 098 

866 745 S59( 220 026; 678: 066 119 082^ 

851 770 943j 244 009- 702] 050 143 065 



33 Deji 




54854 83613 56305 

878 697. 329 

902| 581' 353 

927! 565» 377 

9611 649; 401 

9761 533; 425 

999 617i 449 

55024 601? 473 

048 485! 497 

072 469. 521 

097 463 545 

121 437 569 

145 421; 593 

169 405 617 

194 389 641 



82643 
626 
610 
693 
677 
561 
544 
528 
511 
495 
478 
462 
446 
429 
413 



55218 83373 56665 82396 

242i 356; 689^ 380 

266! 340 713. 363 

a9r 324) 736- 347 

315 308; 760 330 

339 292 784 314 

363 276 808 297 

S88i 260t 832 281 

412: 244 856 264 

436 228 880 248 



460, 212 904 231 
484 195 928 214 
509, 179 952 198 



836 794 9284 269 83964 726 034 167 048i o 
821 819 913! 293 978 750! 017 191 032; 7 



806 844 



792 869 882 342 946 



N 



317 S62 



773 001 215 0151 
799 82985 238 81999 



777 893 866 366 930 823i 969 262, 982 

762 918 851 391 016 847| 953 286| 965 

747 943 836? 416 899 871 936 310l 949 

732 967 820[ 440 883 896i 920 334: 932 



iN.C> N, S N ( S|N. S. W.CS:N. S. 



5P O 5.^ I)pg.i57 Deg.^56 Peg. 55 Deg. 



J3e 



A TABLE OF NATURAL SINES^. 



M 


35 Deg.!36 Deg.\ 


37 Deg." 


38 Deg,|39 Ueg.j 


M 


N. S.N.CSjN. S. 


N.CS.'N. S.,N.CS,,N. S. N.CS* 


N. S.,N.CS| 





57358 


81915'58779;80902;60I82 79864 6I.566'78801 62932,777151 


60 


1 


881 


899i 802' 885v 205 846 589 


783 955 6961 


69 


2 


405 


882 826' 867] 228; 829 612 


765* 977 678| 


58 


3 


429 


866 849 850? 261; 811 635 
848 873 833; 2741 793 658 


747 63000 


660 


57 


4 


453 


729: 022 


641 


56 


5 


477 


832 896| 816- 298i 776. 681 


711 


045 


623 


55 


6 


501 


815 820 799J 321 758! 704 


694 


068 


605 


54 


7 


524 


798i 943 7823 344; 741? 726 


676 


090 


686 


63 


8 


548 


782 967 


765, 367 723 749' 658 


113 


568 


52 


9 


572 


765 990 


748; 390 706 772' 6401 135 


650 


61 


10 


596 


748-59014 


730 414 688 7951 622^ 158 


631 


50 


11 


619 


731 037 


713! 437 671 818| 604 180 


613 


49 


12 


643 


714 061 


696i 460 653 8411 686 203 


494 48 


13 


667 


698 084 


6791 483 635 8641 568 225 


4761 47 


14 


691 


681 108 


662! 506 618 887 550 248^ 458| 46! 


15 


715 


664 131 644' 629 600' 909 ^ 532 


271 439| 45] 


16 


57738 81647S59164, 80627160563 79583 61932 7851463293 7742li 44] 


17 


762 


631S 178 


6101 576 585 956 496, 316 402 


43 


18 


786 


6141 201 


593| 599 6473 978; 4781 338! 384 


42 


19 


810 


5972 226 


676 622 


530:!62001l 4605 361 366 


41 


20 


833 


580' 248 


55S? 645 


512s 024i 442^ 383 347 


40 


21 


857 


563j 272 


641 


668 


4945 046: 424, 406! 329 


39 


22 


881 


546 295 


624 


69 li 477S 069 


405 428 


3101 38] 


23 


904 


530i 318 


507 


714 


459| 092 


387s 451 


292 


37 


24 


923 


613' 342 


489 


738 


441| 115 


369, 473 


273 


36 


25 


952 


496i 365 


472 


761 


4242 138 


351 496 


255 


36 


26 


976 


479i 389 


465S 784 


406| 160 
38^ 183 


333 518 


236i 34] 


27 


999 


462 412! 438? 807 


316 540 


218 


33 


28 


580231 4455 436| 420^ 830 


37ii 206 


297 563 


199 


32 


29 


047 428^ 4591 4031 853 


35^ 229 


279 585 


181 


31 


30 
"31 


070 412 482 
58094 81396 69508 


386) 876 335] 251 


261 


608 
,636^8 


162 


30 

29 


80368?60899 ; 79318i62274 


78243 


77144 


32 


118 


378 629 3511 922| 3005 297 


225; 653 


125 


28 


33 


141 


361 552 334? 945 


282 


320 


206 675 


107 


27 


34 


165 


344 576 316f 968 


264 


342 


18Sl 698 


088 


26 


35 


189i 327. .599 299:- 991 


247 


365 


170? 720 


070 


25 


36 


212 310' 622 282;:61015 


229 


388 


152| 742 


051 


24 


37 


2361 293- 646' 264? 038 


211 


411 


134| 766 


033 


23 


38 


260; 276 669i 247" 061 


193 


433 


lief 787 


014 


22 


39 


283i 259 693 230J 0841 176 


466 


098| 810 


76996 


21 


40 


307 242 716 212? 107| 158 


479 


079|'i 832 


977 20 


J 


330 
354 


225 739 195 


1531 122 


znc> 

524 


061 854 
^ 04S 877 


959 i 19 
940 18 


208 763 178 


•'43 


378 191 786 160° 176! 105 


647 


fcp2T 899 


921! 17 


44 


401; 174 809 143 199| 087 


670l^007l 922 


903' 16 


4S 

^46 

47 


425 157 832; 125 222i 069 


592 


77988' 944 
77970 63966 


884 15 
76866 14 


68449 8114069856 80108 61245 79051 


62615 


472 123- 879, 091 268i 033 


638 


952. 989 


847| 13 


48 


496 106 e02i 073 291 1 015 


660 


934,"64011 


828i 12 


49 


519;" '089 926 056 314 78998 


683 


916 


033 


8io! 11 


50 


543' 072; 949: 038 337: 980 


706 


897 


056 


791 1 10 


51 


667 0553 9721 021 3601 962 


728! 879 


078 


7721 9' 


52 


590 038' 995i 003 383 


944 


751! 861 


100 


754 8 


53 


614 02160019 79986 406 


926 


774 


843 


123 


735 7 


54 


637 004 042 968- 429 


908 


796 


824 


145 


717 6 


55 


66180987i ,065 951. 451 


891 


819 


808 


167 


698 


5 


S6 


684 970] 089; 934? 474 


873 


842 


788 


190 


679 


4 


S7 


708 9531 112; 916; 497 


855 


864 


769 


212 


661 


3 


58 


^31 936] 135i 899j 520 


837 


887 


751 


234 


642 


2 


59 
M 


755 

N.CS 


919] 158' 881-; 543 


819 


909 


733 


256 


623 

N. S. 


I 

M 


N. S.fN.CS.iN. S.jN.OS 


N. S. 


n.cs|n. s. 


N.CS. 




54 Deg.!63 DegA52 Deg. 


61 Deg. 


[so Deg. 


1— 


a^^MB 





















A TABLE OP NATURAL SINES. 



1S7 



40 Deg. 



N. S. N.CS 



64279 
301 
323 
346 
368 
390 
412 
435 
457 
479 
501 
524 
546 
568 
690 
612 



M 



1 

2 

3 

4 

5 

6 

7 

6 

9 

10 
11 
12 
IS 
14 
\5 

16 
17 

18 
19 
20 
21 
22 
23 
24 
25' 
26 
27 
28 
29 
30 

'3164967 
321 989 
33:65011 
34 033 



76604 
586 



64633 
657 
679 
701 
723 
746 
768 
790 
812 
834 
856 
878 
901 
923 
915 



76304165956 
286j 978 
267166000 
248 022 



055 
077 
099 
122 
144 
166 
i88 
210 
232 
264 
276 



41 Deg7T2 Peg. } 43 Deg.l 44 Peg? 

N. S. . N.CSN. S . N.CSiJV. S. N. Cs|n. S.|N.CS 



65606 
628 



567 650 



648 
530 
511 
492 
473 
455 
436 
417 
398 
380 
361 
342 
323 



7547166913 



229 
210 
192 
173 
154 
135 
116 
097 
078 
059 
04l' 



044 
066 
088 
109 
131 
153 
175 
197 
218 
240 
262 



76022 66284 

003! 306 

75984^ 327 

965 349 

946 371 

9271 393 

908 414 

8891 436 

87M 458 

85lj 480 

832| 501 

813 523 

794] 545 

7751 566 

756' 588 



74314)68200 

295j 221 

2761 242 

256; 264 

237 285 

217 306 

198 327 

178! 349 

159; 370 

139i 391 

120j 412 

100! 433 

0801 455 

061? 476 

041j 497 

022; 518 

74002 68539 

73983. 561 

963) 682 

944] 603 

924] 624 

904 645 

685! 666 

865i 688 

846r 709 

826) 730 

806) 751 

787j 772 

767 793 

7471 814 

72S 835 



73135 69466 

116-, 487 

096i 608 

076; 529 

056' 549 

036 670 

016 591 

729961 612 

9761 633 

957? 654 



937 
917 



71934 
914 
894 
873 
853 
833 
813 
792 
772 
752 
732 
711 
691 
671 



46 66298 
47; 320 
481 342 



364 
386 
408 
430 
452 
474 
496 
518 
540 
562 
584 
606 



75738=66610 
719 632 
699 653 
680 675 
661 697 



642 
623 



585 
666 



718 
740 



604 762 



783 
806 



547 827 

528( 848 

609i 870 

490) 891 

4711 913 



N. S. N.CS 




74586 67901 
567 923 
548" 944 
528i 965 
509 987 
489 68008 
470, 029 
451; 051 
431: 072 
412; 093 
392 115 
373 136 
353 157 
334 179 
314 200 

N. s. nTcs 



73412 69172 

393' 193 

373 214 

353 236 

333 256 

SM; 277 

294' 298 

274 319 

254 340 

234 361 

215 382 

195 403 

175 424 

156 445 

135 466 

N. S.'N.CS 



675 

696 

897j 717 

877, 737 . . _ 

857^ 758' 650 

837- 779 630 1 
72817 69800 71610 

797i 821 590 

777^ 8421 569 

767; 862 649 

737i 883! 529 

717:4 9041 608 

6971 9251 488 

677 946 j 468 

6571 966! 447! 

637- 987; 427 

61T70008i 407^ 

597 029 386 

577l 049! 366 

557j 070 345! 

5373 091 325 i 
72517 70112 71305! 

497, 132; 284 

477 153! 264 

467i 1741 243 

437^ 1951 223 

4175 215' 203 

3971 2361 182 

357J 277 

337 298 

3171 319, .^ 

297I 339 080 

277 360! 059 

257J 381; 039 

236; 401! 019 

72216 70422 70998 

196' 443 9781 

176' 463 957 

156 484 937 

136 606 916 

116, 525 896 

095 546 875 

075 667 855 

055 687 834 

035 608 813 

015 628 793 

71995 649 772 

974 670! 752 

954 690 731 

934 711 711 

nT^'n.csn. s. 



'52 

141 
121 
100 



60 
59 
58 
67 
56 
65 
54 
63 
62 
51 

49 
48 
47 
46 

J5 
44 
43 
42] 
4ll 
40^ 
39' 
38 
37; 
36 
35' 
34 
33, 
32 

! 31 

;_30 

i 29 
28 
27 
26 
25 
24 
23 

21 
20 
19 
18 
17 
16 
J5 
14 
13 
12 

10 
9 
8 
7 
€ 

3 
2 



49 Peg. 48 Pe g.i47 Peg. 4 6 Peg..45Deg._ 



m 



6A8 




019 408 619 



Wi 



:l;l >'h\\i 



< ;'■ 



i;i-»:i-rt; 



i':^% i; 



m 



■('i. 



}\^''i' 



■<:!) 



! '' > '. I. 



